数字滤波器的仿真与实现-外文翻译
IIR数字滤波器的设计外文文献以与翻译
IIRDigitaFilterDesignAn important step in the development of a digital filter is the determination of a realizable transfer function G(z) approximating the given frequency response specifications. If an IIR filter is desired,it is also necessary to ensure that G(z) is stable. The process of deriving the transfer function G(z) is called digital filter design. After G(z) has been obtained, the next step is to realize it in the form of a suitable filter structure. In chapter 8,we outlined a variety of basic structures for the realization of FIR and IIR transfer functions. In this chapter,we consider the IIR digital filter design problem. The design of FIR digital filters is treated in chapter 10.First we review some of the issues associated with the filter design problem. A widely used approach to IIR filter design based on the conversion of a prototype analog transfer function to a digital transfer function is discussed next. Typical design examples are included to illustrate this approach. We then consider the transformation of one type of IIR filter transfer function into another type, which is achieved by replacing the complex variable z by a function of z. Four commonly used transformations are summarized. Finally we consider the computer-aided design of IIR digital filter. To this end, we restrict our discussion to the use of matlab in determining the transfer functions.9.1 preliminary considerationsThere are two major issues that need to be answered before one can develop the digital transfer function G(z). The first and foremost issue is the development of a reasonable filter frequency response specification from the requirements of the overall system in which the digital filter is to be employed. The second issue is to determine whether an FIR or IIR digital filter is to be designed. In the section ,we examine these two issues first .Next we review the basic analytical approach to the design of IIR digital filters and then consider the determination of the filter order that meets the prescribed specifications. We also discuss appropriate scaling of the transfer function.9.1.1 Digital Filter SpecificationsAs in the case of the analog filter,either the magnitude and/or the phase(delay) response is specified for the design of a digital filter for most applications. In some situations, the unit sample response or step response may be specified. In most practical applications, the problem of interest is the development of a realizable approximation to a given magnitude response specification. As indicated in section 4.6.3, the phase response of the designed filter can be corrected by cascading it with an allpass section. The design of allpass phase equalizers has received a fair amount of attention in the last few years. We restrict our attention in this chapter to the magnitude approximation problem only. We pointed out in section 4.4.1 that there are four basic types of filters,whose magnitude responses are shown in Figure 4.10. Since the impulse response corresponding to each of these is noncausal and of infinite length, these ideal filters are not realizable. One way of developing a realizable approximation to these filter would be to truncate the impulse response as indicated in Eq.(4.72) for a lowpass filter. The magnitude response of the FIR lowpass filter obtained by truncating the impulse response of the ideal lowpass filter does not have a sharp transition from passband to stopband but, rather, exhibits a gradual "roll-off."Thus, as in the case of the analog filter design problem outlined in section 5.4.1, the magnitude response specifications of a digital filter in the passband and in the stopband are given with some acceptable tolerances. In addition, a transition band is specified between the passband and the stopband to permit the magnitude to drop off smoothly. For example, the magnitude )(j e G of a lowpass filter may be given as shown in Figure7.1. As indicated in the figure, in the passband defined by 0p ωω≤≤, we require that the magnitude approximates unity with an error of p δ±,i.e.,p p j p for e G ωωδδω≤+≤≤-,1)(1.In the stopband, defined by πωω≤≤s ,we require that the magnitude approximates zero with an error of i s ,δ.e.,,)(s j e G δω≤ forπωω≤≤s . The frequencies p ω and s ω are , respectively, called the passband edge frequency and the stopband edge frequency. The limits of the tolerances in the passband and stopband, p δ and s δ, are usually called the peak ripple values. Note that the frequency response )(ωj e G of a digital filter is a periodic function of ω,and the magnitude response of a real-coefficient digital filter is an even function ofω. As a result, the digital filter specifications are given only for the range πω≤≤0.Digital filter specifications are often given in terms of the loss function,)(log 20)(10ωωζj e G -=, in dB. Here the peak passband ripplep α and the minimum stopband attenuations α are given in dB,i.e., the loss specifications of a digitalfilter are given bydB p p )1(log 2010δα--=,dB s s )(log 2010δα-=.9.1 Preliminary ConsiderationsAs in the case of an analog lowpass filter, the specifications for a digital lowpass filter may alternatively be given in terms of its magnitude response, as in Figure 7.2. Here the maximum value of the magnitude in the passband is assumed to be unity, and themaximum passband deviation, denoted as 1/21ε+,is given by the minimum value of the magnitude in the passband. The maximum stopband magnitude is denoted by 1/A.For the normalized specification, the maximum value of the gain function or the minimum value of the loss function is therefore 0 dB. The quantity max α given bydB )1(log 20210max εα+=Is called the maximum passband attenuation. Forp δ<<1, as is typically the case, itcan be shown thatp p αδα2)21(log 2010max ≅--≅ The passband and stopband edge frequencies, in most applications, are specified in Hz, along with the sampling rate of the digital filter. Since all filter design techniques are developed in terms of normalized angular frequencies p ω and s ω,the sepcified critical frequencies need to be normalized before a specific filter design algorithm can be applied. Let T F denote the sampling frequency in Hz, and F P and F s denote, respectively,the passband and stopband edge frequencies in Hz. Then the normalized angular edge frequencies in radians are given byT F F F F p TpT p p ππω22==Ω= T F F F F s T s T s s ππω22==Ω= 9.1.2 Selection of the Filter TypeThe second issue of interest is the selection of the digital filter type,i.e.,whether an IIR or an FIR digital filter is to be employed. The objective of digital filter design is to develop a causal transfer function H(z) meeting the frequency response specifications. For IIR digital filter design, the IIR transfer function is a real rational function of 1-z . H(z)=N MdNzz d z d d pMz z p z p p ------++++++++ (2211022110)Moreover, H(z) must be a stable transfer function, and for reduced computational complexity, it must be of lowest order N. On the other hand, for FIR filter design, the FIR transfer function is a polynomial in 1-z:∑=-=Nnnz nhzH] [)(For reduced computational complexity, the degree N of H(z) must be as small as possible.In addition, if a linear phase is desired, then the FIR filter coefficients must satisfy the constraint:][][Nnhnh-±=T here are several advantages in using an FIR filter, since it can be designed with exact linear phase and the filter structure is always stable with quantized filter coefficients. However, in most cases, the order N FIR of an FIR filter is considerably higher than the order N IIR of an equivalent IIR filter meeting the same magnitude specifications. In general, the implementation of the FIR filter requires approximately N FIR multiplications per output sample, whereas the IIR filter requires 2N IIR+1 multiplications per output sample. In the former case, if the FIR filter is designed with a linear phase, then the number of multiplications per output sample reduces to approximately (N FIR+1)/2. Likewise, most IIR filter designs result in transfer functions with zeros on the unit circle,and the cascade realization of an IIR filter of orderIIRN with all of the zeros on the unitcircle requires [(3IIRN+3)/2] multiplications per output sample. It has been shown that for most practical filter specifications, the ratio N FIR/N IIR is typically of the order of tens or more and, as a result, the IIR filter usually is computationally more efficient[Rab75]. However ,if the group delay of the IIR filter is equalized by cascading it with an allpass equalizer, then the savings in computation may no longer be that significant [Rab75]. In many applications, the linearity of the phase response of the digital filter is not an issue,making the IIR filter preferable because of the lower computational requirements.9.1.3 Basic Approaches to Digital Filter DesignIn the case of IIR filter design, the most common practice is to convert the digital filter specifications into analog lowpass prototype filter specifications, and then to transform it into the desired digital filter transfer function G(z). This approach has been widely used for many reasons:(a) Analog approximation techniques are highly advanced.(b) They usually yield closed-form solutions.(c) Extensive tables are available for analog filter design.(d) Many applications require the digital simulation of analog filters.In the sequel, we denote an analog transfer function as)()()(s D s P s H a a a =, Where the subscript "a" specifically indicates the analog domain. The digital transfer function derived form H a (s) is denoted by)()()(z D z P z G = The basic idea behind the conversion of an analog prototype transfer function H a (s) into a digital IIR transfer function G(z) is to apply a mapping from the s-domain to the z-domain so that the essential properties of the analog frequency response are preserved. The implies that the mapping function should be such that(a) The imaginary(j Ω) axis in the s-plane be mapped onto the circle of the z-plane.(b) A stable analog transfer function be transformed into a stable digital transfer function.To this end,the most widely used transformation is the bilinear transformation described in Section 9.2.Unlike IIR digital filter design,the FIR filter design does not have any connection with the design of analog filters. The design of FIR filter design does not have anyconnection with the design of analog filters. The design of FIR filters is therefore based on a direct approximation of the specified magnitude response,with the often added requirement that the phase response be linear. As pointed out in Eq.(7.10), a causal FIR transfer function H(z) of length N+1 is a polynomial in z -1 of degree N. The corresponding frequency response is given by∑=-=N n n j j en h e H 0][)(ωω.It has been shown in Section 3.2.1 that any finite duration sequence x[n] of length N+1 is completely characterized by N+1 samples of its discrete-time Fourier transfer X(ωj e ). As a result, the design of an FIR filter of length N+1 may be accomplished by finding either the impulse response sequence {h[n]} or N+1 samples of its frequency response )H(e j ω. Also, to ensure a linear-phase design, the condition of Eq.(7.11) must be satisfied. Two direct approaches to the design of FIR filters are the windowed Fourier series approach and the frequency sampling approach. We describe the former approach in Section 7.6. The second approach is treated in Problem 7.6. In Section 7.7 we outline computer-based digital filter design methods.作者：Sanjit K.Mitra国籍：USA出处：Digital Signal Processing -A Computer-Based Approach 3eIIR数字滤波器的设计在一个数字滤波器发展的重要步骤是可实现的传递函数G（z）的接近给定的频率响应规格。
基于matlab的数字滤波器的设计和仿真
西安欧亚学院本科毕业论文（设计）题目：学生姓名：指导教师：所在分院：专业：班级：二O一一年四月基于Matlab的数字滤波器的设计与仿真摘要:传统的数字滤波器的设计关键词：.FDAtools;FIR数字滤波器;simullink仿真;窗函数法;频率采样法Matlab-based digital filter design and simulationAbstract:The traditional digital filter, the design process of complex computing workload big, filtering properties, affected it hard to adjust the application. This paper introduces a kind of Filter matlab FDAtools Analysis and Design tools themselves and order the Filter Tool (by rapid and effective Design) of software component Design method of traditional digital Filter. Using matlab language is given for program design and use of signal processing fdatool toolbox of tools for interface design of the specific steps. Matlabdesign filter, can always contrast the design requirements and filter characteristics, easy adjustment parameters greatly reduced the workload, be helpful for the optimization design of fir. This paper also introduces how to use matlab simulation software simulink filters the design of simulation.Keywords: FDAtools;FIR digital filters; simullink;simulstion window function method;frequency sampling method第1章绪论 (1)1.1 课题背景及目的 (1)1.2 国内外研究现状 (1)1.3 研究内容 (1)1.4 研究方法 (2)1.5 Matlab简介 (2)1.6 Matlab的特点 (2)1.7 Matlab的系统组成 (2)1.8 论文提纲 (3)第2章数字滤波器基本原理 (4)2.1 数字滤波器原理 (4)2.2 数字滤波器分类 (4)2.3 数字滤波器技术要求 (6)第3章FIR数字滤波器的设计 (9)3.1 窗函数法设计FIR数字滤波器 (9)3.1.1 窗函数法设计原理 (9)3.1.2 FIR数字滤波器的设计实例 (10)3.2 频率采样法设计FIR数字滤波器 (11)3.2.1 频率采样法的基本思想 (13)3.2.2 FIR数字滤波器的设计实例 (14)3.3 窗函数法和频率采样法 (18)3.3.1 通过实例对两种方法做比较 (18)3.3.2 两种方法设计带通滤波器 (20)第4章应用Simulink对FIR数字滤波器滤波 (22)4.1 FDATool和Simulink工具 (22)4.1.1 FDATool的介绍 (22)4.1.2 FDATool的使用 (22)4.2 Simulink工具 (22)4.2.1 Simulink的介绍 (22)4.2.2 Simulink的使用 (22)4.3 利用FDATool和Simulink设计FIR数字滤波器 (23)4.4 数字滤波器的仿真及实现 (25)第5章浅析用MATLAB辅助DSP实现FIR数字滤波器 (29)5.1 MATLAB辅助DSP开发简介 (29)5.2 MATLAB与CCS及目标DSP间的连接 (29)5.3 MATLAB辅助DSP实现FIR过程 (30)第6章结论 (31)致辞 (32)参考文献 (33)附录:论文中所提到的程 (34)第1章绪论1.1课题背景及目的1.1.1 背景来源本文FIR数字滤波器设计时Matlab软件使用的是Matlab7.0。
DSP滤波器中英文对照外文翻译文献
中英文对照外文翻译文献(文档含英文原文和中文翻译)译文:GA算法优化IIR滤波器的设计摘要本文提出了运用遗传算法(GA)来优化无限脉冲响应数字滤波器(IIR)的设计。
IIR滤波器本质上是一个递归响应的数字滤波器。
由于IIR 数字滤波器的表面误差通常是非线性的和多峰的，而全局优化技术需要避免局部最小值。
本文提出了启发式方式来设计IIR滤波器。
GA是组合优化问题中一种功能强大的全局优化算法，该论文发现IIR数字滤波器的最佳系数可以通过GA 优化。
该设计提出低通和高通IIR数字滤波器的设计，以提供过渡频带的估计值。
结果发现，所计算出的值比可用于过滤器的在MATLAB设计FDA工具更优化。
举个例子，采用的仿真结果表明在过渡带和均方误差(MSE)的改善。
零极点的位置也被提出来用来描述系统的的稳定性，以便将结果与模拟退火(SA)的方法相比较。
关键词：数字滤波器;无限冲激响应(IIR);遗传算法(GA);优化1.说明在过去的几十年中的数字信号处理(DSP)领域已经成长太重要的理论和技术。
在DSP中，有两个重要的类型系统。
第一类型的系统是执行信号滤波的时域，因此它被称为数字滤波器。
第二类型的系统提供的信号表示频域，被称为频谱分析仪。
数字滤波是DSP的最有力的工具之一。
数字滤波器能够性能规格，最好的同时也是极其困难的，而且不可能的是，先用模拟滤波器实现。
另外，数字滤波器的特性，可以很容易地在软件控制下发生变化。
数字滤波器被分类为有限持续时间脉冲响应(FIR)滤波器或无限持续时间脉冲响应(IIR)滤波器，这取决于该系统的脉冲响应的形式。
在FIR系统中，脉冲响应序列是有限的持续时间，即，它具有非零项的数量有限。
数字无限脉冲响应(IIR)滤波器通常可以提供比其等效有限脉冲响应(FIR)滤波器更好的性能和更少的计算成本，并已成为越来越感兴趣的目标。
但是，由于IIR滤波器的误差表面通常是非线性的，多式联运，传统的基于梯度的设计方法可以很容易地陷入错误的表面。
数字滤波器文献翻译
文献翻译外文：Digital filterIn electronics, computer science and mathematics, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is an electronic circuit operating on continuous-time analog signals. An analog signal may be processed by a digital filter by first being digitized and represented as a sequence of numbers, then manipulated mathematically, and then reconstructed as a new analog signal (see digital signal processing). In an analog filter, the input signal is "directly" manipulated by the circuit.A digital filter system usually consists of an analog-to-digital converter to sample the input signal, followed by a microprocessor and some peripheral components such as memory to store data and filter coefficients etc. Finally a digital-to-analog converter to complete the output stage. Program Instructions (software) running on the microprocessor implement the digital filter by performing the necessary mathematical operations on the numbers received from the ADC. In some high performance applications, an FPGA or ASIC is used instead of a general purpose microprocessor, or a specialized DSP with specific paralleled architecture for expediting operations such as filtering.Digital filters may be more expensive than an equivalent analog filter due to their increased complexity, but they make practical many designs that are impractical or impossible as analog filters. Since digital filters use a sampling process and discrete-time processing, theyexperience latency (the difference in time between the input and the response), which is almost irrelevant in analog filters.Digital filters are commonplace and an essential element of everyday electronics such as radios, cellphones, and stereo receivers.Characterization of digital filtersA digital filter is characterized by its transfer function, or equivalently, its difference equation. Mathematical analysis of the transfer function can describe how it will respond to any input. As such, designing a filter consists of developing specifications appropriate to the problem (for example, a second-order low pass filter with a specific cut-off frequency), and then producing a transfer function which meets the specifications.The transfer function for a linear, time-invariant, digital filter can be expressed as a transfer function in the Z-domain; if it is causal, then it has the form:where the order of the filter is the greater of N or M. See Z-transform's LCCD equation for further discussion of this transfer function.This is the form for a recursive filter with both the inputs (Numerator) and outputs (Denominator), which typically leads to an IIR infinite impulse response behaviour, but if the denominator is made equal to unity i.e. no feedback, then this becomes an FIR or finite impulse response filter.Analysis techniquesA variety of mathematical techniques may be employed to analyze the behaviour of a given digital filter. Many of these analysis techniques may also be employed in designs, and often form the basis of a filter specification.Typically, one analyzes filters by calculating how the filter will respond to a simple input such as an impulse response. One can then extend this information to visualize the filter's response to more complex signals. Riemann spheres have been used, together with digital video, for this purpose.Impulse responseThe impulse response, often denoted h[k] or h k, is a measurement of how a filter will respond to the Kronecker delta function. For example, given a difference equation, one would set x0 = 1 and x k = 0 for and evaluate. The impulse response is a characterization of the filter's behaviour. Digital filters are typically considered in two categories: infinite impulse response (IIR) and finite impulse response (FIR). In the case of linear time-invariant FIR filters, the impulse response is exactly equal to the sequence of filter coefficients:IIR filters on the other hand are recursive, with the output depending on both current and previous inputs as well as previous outputs. The general form of the an IIR filter is thus:Plotting the impulse response will reveal how a filter will respond to a sudden, momentary disturbance.Difference equationIn discrete-time systems, the digital filter is often implemented by converting the transfer function to a linear constant-coefficient difference equation (LCCD) via the Z-transform. The discrete frequency-domain transfer function is written as the ratio of two polynomials. For example:This is expanded:and divided by the highest order of z:The coefficients of the denominator, a k, are the 'feed-backward' coefficients and the coefficients of the numerator are the 'feed-forward' coefficients, b k. The resultant linear difference equation is:or, for the example above:rearranging terms:then by taking the inverse z-transform:and finally, by solving for y[n]:This equation shows how to compute the next output sample, y[n], in terms of the past outputs, y[n−p], the present input, x[n], and the past inputs, x[n−p]. Applying the filter to an input in this form is equivalent to a Direct Form I or II realization, depending on the exact order of evaluation.Filter designMain article: Filter designThe design of digital filters is a deceptively complex topic.[1] Although filters are easily understood and calculated, the practical challenges of their design and implementation are significant and are the subject of much advanced research.There are two categories of digital filter: the recursive filter and the nonrecursive filter. These are often referred to as infinite impulseresponse (IIR) filters and finite impulse response (FIR) filters, respectively.[2]Filter realizationAfter a filter is designed, it must be realized by developing a signal flow diagram that describes the filter in terms of operations on sample sequences.A given transfer function may be realized in many ways. Consider how a simple expression such as ax+ bx+ c could be evaluated –one could also compute the equivalent x(a + b) + c. In the same way, all realizations may be seen as "factorizations" of the same transfer function, but different realizations will have different numerical properties. Specifically, some realizations are more efficient in terms of the number of operations or storage elements required for their implementation, and others provide advantages such as improved numerical stability and reduced round-off error. Some structures are better for fixed-point arithmetic and others may be better for floating-point arithmetic.Direct Form IA straightforward approach for IIR filter realization is Direct Form I, where the difference equation is evaluated directly. This form is practical for small filters, but may be inefficient and impractical (numerically unstable) for complex designs.[3] In general, this form requires 2N delay elements (for both input and output signals) for a filter of order N.Direct Form IIThe alternate Direct Form II only needs N delay units, where N is the order of the filter –potentially half as much as Direct Form I. This structure is obtained by reversing the order of the numerator and denominator sections of Direct Form I, since they are in fact two linear systems, and the commutativity property applies. Then, one will notice that there are two columns of delays (z− 1) that tap off the center net, and these can be combined since they are redundant, yielding the implementation as shown below.The disadvantage is that Direct Form II increases the possibility of arithmetic overflow for filters of high Q or resonance.[4]It has been shown that as Q increases, the round-off noise of both direct form topologies increases without bounds.[5]This is because, conceptually, the signal is first passed through an all-pole filter (which normally boosts gain at the resonant frequencies) before the result of that is saturated, then passed through an all-zero filter (which often attenuates much of what the all-pole half amplifies).Cascaded second-order sectionsA common strategy is to realize a higher-order (greater than 2) digital filter as a cascaded series of second-order "biquadratric" (or "biquad") sections[6] (see digital biquad filter). Advantages of this strategy is that the coefficient range is limited. Cascading direct form II sections result in N delay elements for filter order of N. Cascading direct form I sections result in N+2 delay elements since the delay elements of the input of any section (except the first section) are a redundant with the delay elements of the output of the preceding section.文献翻译译文：数字滤波在电子学、计算机科学和数学中，数位滤波器是在一个系统上执行一个采样，在离散时间上对信号进行的数学运算，以减少或增加这种信号的某些方面。
外文翻译--数字滤波器的仿真与实现
毕业设计(论文)外文资料翻译院系电子信息工程专业电子信息工程学生姓名班级学号外文出处百度文库附件：1.外文资料翻译译文（约3000汉字）；2.外文资料原文(与课题相关的1万印刷符号左右)。
英文原文The simulation and the realization of the digital filter With the information age and the advent of the digital world, digital signal processing has become one of today's most important disciplines and door technology. Digital signal processing in communications, voice, images, automatic control, radar, military, aerospace, medical and household appliances, and many other fields widely applied. In the digital signal processing applications, the digital filter is important and has been widely applied.1、figures Unit on :Analog and digital filtersIn signal processing, the function of a filter is to remove unwanted parts of the signal, such as random noise, or to extract useful parts of the signal, such as the components lying within a certain frequency range.The following block diagram illustrates the basic idea.There are two main kinds of filter, analog and digital. They are quite different in their physical makeup and in how they work. An analog filter uses analog electronic circuits made up from components such as resistors, capacitors and op amps to produce the required filtering effect. Such filter circuits are widely used in such applications as noise reduction, video signal enhancement, graphic equilibrium in hi-fi systems, and many other areas. There are well-established standard techniques for designing an analog filter circuit for a given requirement. At all stages, the signal being filtered is an electrical voltage or current which is the direct analogue of the physical quantity (e.g. a sound or video signal or transducer output) involved. A digital filter uses a digital processor to performnumerical calculations on sampled values of the signal. The processor may be a general-purpose computer such as a PC, or a specialized DSP (Digital Signal Processor) chip. The analog input signal must first be sampled and digitized using an ADC (analog to digital converter). The resulting binary numbers, representing successive sampled values of the input signal, are transferred to the processor, which carries out numerical calculations on them. These calculations typically involve multiplying the input values by constants and adding the products together. If necessary, the results of these calculations, which now represent sampled values of the filtered signal, are output through a DAC (digital to analog converter) to convert the signal back to analog form.Note that in a digital filter, the signal is represented by a sequence of numbers, rather than a voltage or current.The following diagram shows the basic setup of such a system.Unit refers to the input signals used to filter hardware or software. If the filter input, output signals are separated, they are bound to respond to the impact of the Unit is separated, such as digital filters filter definition. Digital filter function, which was to import sequences X transformation into export operations through a series Y.According to figures filter function 24-hour live response characteristics, digital filters can be divided into two, namely, unlimited long live long live the corresponding IIR filter and the limited response to FIR filters. IIR filters have theadvantage of the digital filter design can use simulation results, and simulation filter design of a large number of tables may facilitate simple. It is the shortcomings of the nonlinear phase; Linear phase if required, will use the entire network phase-correction. Image processing and transmission of data collection is required with linear phase filters identity. And FIR linear phase digital filter to achieve, but an arbitrary margin characteristics. Impact from the digital filter response of the units can be divided into two broad categories : the impact of the limited response (FIR) filters, and unlimited number of shocks to (IIR) digital filters.FIR filters can be strictly linear phase, but because the system FIR filter function extremity fixed at the original point, it can only use the higher number of bands to achieve their high selectivity for the same filter design indicators FIR filter called band than a few high-IIR 5-10 times, the cost is higher, Signal delay is also larger. But if the same linear phase, IIR filters must be network-wide calibration phase, the same section also increase the number of filters and net work complexity. FIR filters can be used the recursive method, not in a limited precision of a shock, and into the homes and quantitative factors of uncertainty arising from the impact of errors than IIR filter small number, and FIR filter can be used FFT algorithms, the computational speed. But unlike IIR filter can filter through the simulation results, there is no ready-made formula FIR filter must use computer-aided design software (such as MATLAB) to calculate. So, a broader application of FIR filters, and IIR filters are not very strict requirements on occasions.Unit from sub-functions can be divided into the following four categories :(1) Low-filter (LPF);(2) high-filter (HPF);(3) belt-filter (BPF);(4) to prevent filter (BSF).The following chart dotted line for the ideals of the filter frequency characteristics :2、MATLAB introducedMATLAB is a matrix laboratory (Matrix Laboratory) is intended. In addition to an excellent value calculation capability, it also provides professional symbols terms, word processing, visualization modeling, simulation and real-time control functions. MATLAB as the world's top mathematical software applications, with a strong engineering computing, algorithms research, engineering drawings, applications development, data analysis and dynamic simulation, and other functions, in aerospace, mechanical manufacturing and construction fields playing an increasingly important role. And the C language function rich, the use of flexibility, high-efficiency goals procedures. High language both advantages aswell as low level language features. Therefore, C language is the most widely used programming language. Although MATLAB is a complete, fully functional programming environment, but in some cases, data and procedures with the external environment of the world is very necessary and useful. Filter design using MATLAB, could be adjusted with the design requirements and filter characteristics of the parameters, visual simple, greatly reducing the workload for the filter design optimization.In the electricity system protection and secondary computer control, many signal processing and analysis are based on are certain types sinusoidal wave and the second harmonics of the system voltage and current signals (especially at D process), are mixed with a variety of complex components, the filter has been installed power system during the critical components. Current computer protection and the introduction of two digital signal processing software main filter. Digital filter design using traditional cumbersome formula, the need to change the parameters after recalculation, especially in high filters, filter design workload. Uses MATLAB signal processing boxes can achieve rapid and effective digital filter design and simulation.MATLAB is the basic unit of data matrix, with its directives expression mathematics, engineering, commonly used form is very similar, it is used to solve a problem than in MATLAB C, Fortran and other languages End precision much the same thing. The popular MATLAB 5.3/Simulink3.0 including hundreds of internal function with the main pack and 30 types of tool kits (Toolbox). kits can be divided into functional tool kits and disciplines toolkit. MATLAB tool kit used to expand the functional symbols terms, visualization modeling simulation, word processing and real-time control functions. professional disciplines toolkit is a stronger tool kits, tool kits control, signal processing tool kit, tool kits, etc. belonging to such communicationsMATLAB users to open widely welcomed. In addition to the internal function, all the packages MATLAB tool kits are readable document and the document could be amended, modified or users through original program the construction of new procedures to prepare themselves for kits.3、Digital filter designDigital filter design of the basic requirementsDigital filter design must go through three steps :(1) Identification of indicators : In the design of a filter, there must be some indicators. These indicators should be determined on the basis of the application. In many practical applications, digital filters are often used to achieve the frequency operation. Therefore, indicators in the form of general jurisdiction given frequency range and phase response. Margins key indicators given in two ways. The first is absolute indicators. It provides a function to respond to the demands of the general application of FIR filter design. The second indicator is the relative indicators. Its value in the form of answers to decibels. In engineering practice, the most popular of such indicators. For phase response indicators forms, usually in the hope that the system with a linear phase frequency bands human. Using linear phase filter design with the following response to the indicators strengths：①it only contains a few algorithms, no plural operations；②there is delay distortion, only a fixed amount of delay; ③the filter length N (number of bands for N-1), the volume calculation for N/2 magnitude.(2) Model approach : Once identified indicators can use a previous study of the basic principles and relationships, a filter model to be closer to the target system.(3) Achieved : the results of the above two filters, usually by differential equations, system function or pulse response to describe. According to this description of hardware or software used to achieve it.4、Introduction of DSPToday, DSP is widely used in the modern techno logy and it has been the key part of many products and played more and mo re important role in our daily life Recently, Northwestern Poly technical University Aviation Microelectronic Center has completed the design of digital signal processor co re NDSP25, which is aiming at TM S320C25 digital signal processor of Texas Instrument TM S320 series. By using top 2dow n design flow NDSP25 is compatible with instruction and interface timing of TM S320C25.Digital signal processors (DSP) is a fit for real-time digital signal processing for high-speed dedicated processors, the main variety used for real-time digital signal processing to achieve rapid algorithms. In today's digital age background, the DSP has become the communications, computer, and consumer electronics products, and other fields based device.Digital signal processors and digital signal processing is inseparably, we usually say "DSP" can also mean the digital signal processing (Digital Signal Processing), is that in this digital signal processors Lane. Digital signal processing is a cover many disciplines applied to many areas and disciplines, refers to the use of computers or specialized processing equipment, the signals in digital form for the collection, conversion, recovery, valuation, enhancement, compression, identification, processing, the signals are compliant form. Digital signal processors for digital signal processing devices, it is accompanied by a digital signal processing to produce. DSP development process is broadly divided into three phases : the 20th century to the 1970s theory that the 1980s and 1990s for the development of products. Before the emergence of the digital signal processing in the DSP can only rely on microprocessors (MPU) to complete. However, the advantage of lower high-speed real-time processing can not meet the requirements. Therefore, until the 1970s, a talent made based DSP theory and algorithms. With LSI technology development in 1982 was the first recipient of the world gave birth to the DSP chip. Years later, the second generation based on CMOS工艺DSP chips have emerged. The late 1980s, the advent of the third generation of DSP chips. DSP is the fastest-growing 1990s, there have been four successive five-generation and the generation DSP devices. After 20 years of development, the application of DSP products has been extended to people's learning, work and all aspects of life and gradually become electronics products determinants.中文翻译数字滤波器的仿真与实现随着信息时代和数字世界的到来，数字信号处理已成为当今一门极其重要的学科和技术领域。
数字滤波器外文翻译
数字滤波器数字滤波器是对数字信号进行滤波处理以得到期望的响应特性的离散时间系统。
作为一种电子滤波器，数位滤波器与完全工作在模拟信号域的模拟滤波器不同。
数字滤波器工作在数字信号域，它处理的对象是经由采样器件将模拟信号转换而得到的数字信号。
数字滤波器的工作方式与模拟滤波器也完全不同：后者完全依靠电阻、电容、晶体管等电子元件组成的物理网络实现滤波功能；而前者是通过数字运算器件对输入的数字信号进行运算和处理，从而实现设计要求的特性。
数字滤波器理论上可以实现任何可以用数学算法表示的滤波效果。
数字滤波器的两个主要限制条件是它们的速度和成本。
数字滤波器不可能比滤波器内部的计算机的运算速度更快。
但是随着集成电路成本的不断降低，数字滤波器变得越来越常见并且已经成为了如收音机、蜂窝电话、立体声接收机这样的日常用品的重要组成部分。
数字滤波器一般由寄存器、延时器、加法器和乘法器等基本数字电路实现。
随着集成电路技术的发展，其性能不断提高而成本却不断降低，数字滤波器的应用领域也因此越来越广。
按照数字滤波器的特性，它可以被分为线性与非线性、因果与非因果、无限脉冲响应（IIR）与有限脉冲响应（FIR）等等。
其中，线性时不变的数字滤波器是最基本的类型；而由于数字系统可以对延时器加以利用，因此可以引入一定程度的非因果性，获得比传统的因果滤波器更灵活强大的特性；相对于IIR滤波器，FIR滤波器有着易于实现和系统绝对稳定的优势，因此得到广泛的应用；对于时变系统滤波器的研究则导致了以卡尔曼滤波为代表的自适应滤波理论数字滤波器具有比模拟滤波器更高的精度，甚至能够实现后者在理论上也无法达到的性能。
例如，对于数字滤波器来说很容易就能够做到一个1000Hz 的低通滤波器允许999Hz 信号通过并且完全阻止1001Hz 的信号，模拟滤波器无法区分如此接近的信号。
数字滤波器相比模拟滤波器有更高的信噪比。
这主要是因为数字滤波器是以数字器件执行运算，从而避免了模拟电路中噪声（如电阻热噪声）的影响。
外文文献翻译(基于单片机的数字滤波器设计
毕业设计(论文）外文文献翻译院系：信息工程学院年级专业: 电子信息工程姓名：装化学号: 20122450236附件: digital filter design外文文献：digital filter designAbstract：With the information age and the advent of the digital world, digital signal processing has become one of today's most important disciplines and door technology。
Digital signal processing in communications，voice, images, automatic control, radar, military, aerospace, medical and household appliances，and many other fields widely applied。
In the digital signal processing applications, the digital filter is important and has been widely applied。
Keyword：SCM; Proteus, C language；Digital filter1、figures Unit on ：Analog and digital filtersIn signal processing，the function of a filter is to remove unwanted parts of thesignal, such as random noise，or to extract useful parts of the signal, such as the components lying within a certain frequency range.The following block diagram illustrates the basic idea.There are two main kinds of filter，analog and digital. They are quite different in their physical makeup and in how they work. An analog filter uses analog electronic circuits made up from components such as resistors, capacitors and op amps to produce the required filtering effect。
数字滤波器概述(英文版)
4、 The classification of digital filter There are many types of filter，and the method of classification is different.
1、From the functional point:LPF、BPF、HPF、 BSF. 2、From the implementationmethod on：FIR,IIR 3、From the perspective of design method : Butterworth、Chebyshev、Ellips. 4、From the processing of signal：Classical filter 、Modern filter
The block diagram and flow chart are as follows ：
x(n) b0 a1 a2
z-1 z-1
y(n)
x(n) b0 a1 a2
z-1 z-1
y(n)
Explain：We can tell the operation steps and operation structure of the system through the flow chart or diagram. We use flow chart to analyse the structure of digital filters.
The introduction of digital filter
Digital filter
1、 What is the digital filter
definition：Digital filter is a special kind Discrete— time systems described by differential Equations. function： Change the input sequence into the output Sequence by certain operations.And different processing methods determine different implementation structure of the filter.
数字滤波器中英文对照外文翻译文献
中英文对照翻译基于VB和Matlab的数字滤波器的设计摘要数字信号处理的核心是数字滤波器的设计。
目前，大多数数字滤波器是基于Matlab这种高性能的数值计算并提供强大的图形显示功能的软件。
MATLAB广泛应用于工程计算，数值分析等多个领域，但它不善于开发接口。
在本文中，将用VB与Matlab混合编程的方法引入到设计数字滤波器中。
集成的软件可以利用VB 和Matlab的最大优势，实现过程表明，该方法简单，方便。
关键词:数字滤波器，Visual Basic，MATLAB，组件对象模型。
1.引言如今，滤波器在相关的电子系统中很重要，因为他们存在于几乎所有的电子系统。
例如，通信系统中广泛利用滤波器的将噪声和所需信号区分开来。
电源供应器使用滤波器来滤除纹波和改善直流信号的质量。
音频均衡器使用过滤器来放大或衰减频段的音频范围，音频质量的提高取决于房间的声学特性。
数字视频由于编码和传输，需要将数字滤波器接入噪声信道，以减少噪声，依此类推。
然而，滤波器的设计是一个密集的计算任务，需要一个大量数值计算得到的滤波器传递函数的任一参数或为一个滤波电路实现的元素的值。
另外，在日常生活中，电脑的使用已经很普及。
因此，计算机软件开发已经成为技术发展的一个重要组成部分。
教育很大部分受这个发展的影响。
今天，大量的软件包可用于设计滤波器，Matlab便是其中之一。
Matlab是由Mathworks公司开发，是一款高性能的数值计算软件，并提供图形显示的强大功能，它被广泛应用于工程计算，数值分析等领域。
现在任何一所大学或工业都在使用Matlab，并且在电路和系统的设计等许多其它事情都会用到。
其中，Matlab的主要特点是，它的一套工具箱在滤波器的设计中都可以使用。
不足的是，使用这些工具箱，需要相当长的时间去掌握它们，新手才能使用它们。
更重要的是，Matlab不善于开发接口。
相反，VB中有一个友好的设计用户界面和开发应用程序，但它不能够计算，尤其是在数字滤波器的设计中。
数字滤波器设计(国外通俗英文版)
/rcristi/eo3404/c-filters/videos/chapter2-seg1_media/chapter2-seg1-0.wmv
In the typical filtering problem we want to separate a signal from an additive disturbance. In general within the frequency spectrum we can see frequencies in which the signal is dominant and frequencies where the noise is dominant. This is shown in the figure below.
Frequency Response of a Non Ideal Filter
We can immediately see the differences between the two frequency responses. In the non Ideal case the frequency response in the Stop Band is small, but not zero; the frequency response in the Pass Band is not exactly a constant but it has a ripple. Finally there is also a transition region between the Pass Band and the Stop Band. It turns out that (as we will see) the narrower the Transition region (ie the sharper the transition between Passband and Stopband) the higher the complexity of the filter.
IIR数字滤波器的设计外文翻译
IIR数字滤波器的设计数字滤波器发展一个重要步骤是可实现的传递函数G(z)的接近给定频率响应规格的测定，同时若要IIR稳定也有必要确定G(z)稳定性。
该推算传递函数G(z)的过程称为数字滤波器的设计。
获得G(z)函数参数值后，下一步就是实现一个合格的过滤器结构形式。
在第八章，我们概述一系列为实现FIR和IIR各种功能的实现基本结构。
在这一章中，首先考虑了IIR数字滤波器的设计问题，FIR 数字滤波器的设计是在第10章处理。
首先，我们回顾一些滤波器设计问题相关的问题，下文讨论了一种广泛使用的设计IIR滤波器的方法（基于原型模拟到数字的转换传递函数）。
并用典型的设计实例来说明这种方法，然后考虑到一种IIR滤波器的转换它是由一个函数代替复杂的变量Z达到类型转换，对四种常用的转换进行了总结，最后，考虑使用计算机辅助设计IIR数字滤波器，为此，我们限制MATLAB在确定传递函数的使用讨论。
9.1初步考虑在回答发展数字传递函数G(z)之前有两个需要回答的问题，首要的问题是一个合理的滤波器的频率响应规格从整个系统中数字滤波器将被使用的要求发展，第二个问题是要确定所设计的是FIR还是IIR数字滤波器。
在这一节中，我们首先诊察了这两个问题，接下来，我们回顾到的IIR滤波器设计的基本分析方法，然后再考虑过滤器符合规格测定的顺序，讨论了适当的传递函数缩放比例。
9.1.1数字过滤器的规格如模拟过滤器的例子中，无论是规模和/或相位（延迟）响应对于大多数应用数字滤波器都是需要指定的。
在某些情况下，可能被指定的是单位样值响应或跃阶响应，大多实际应用中，利益问题是由一个实现逼近到一个给定的幅度响应规范的发展。
如第4.6.3节，所设计的滤波器可以通过级联与全通网络纠正相位响应。
全通相位均衡器的设计最近几年接受了相当数量的关注。
在这一章节，限制讨论了幅度逼近问题，我们在第4.4.1节指出，有四种基本类型的过滤器，其幅度如图4.10所示，由于脉冲响应对应于所有这些都是非因果和无限长，这些理想过滤器并不是可以实现的，一种实现近似于这种过滤器的方法是截断的脉冲响应，如图所示。
数字滤波器外文翻译
中文5590字毕业设计（外文翻译材料）2009年6月学 院： 专 业： 学生姓名： 指导教师： 电气与电子工程学院 电子信息工程0503DIGITAL FILTERSDigital filtering is one of the most powerful tools of DSP. Apart from the obvious advantages of virtually eliminating errors in the filter associated with passive component fluctuations over time and temperature, op amp drift (active filters), etc., digital filters are capable of performance specifications that would, at best, be extremely difficult, if not impossible, to achieve with an analog implementation. In addition, the characteristics of a digital filter can be easily changed under software control. Therefore, they are widely used in adaptive filtering applications in communications such as echo cancellation in modems, noise cancellation, and speech recognition.The actual procedure for designing digital filters has the same fundamental elements as that for analog filters. First, the desired filter responses are characterized, and the filter parameters are then calculated. Characteristics such as amplitude and phase response are derived in the same way. The key difference between analog and digital filters is that instead of calculating resistor, capacitor, and inductor values for an analog filter, coefficient values are calculated for a digital filter. So for the digital filter, numbers replace the physical resistor and capacitor components of the analog filter. These numbers reside in a memory as filter coefficients and are used with the sampled data values from the ADC to perform the filter calculations.The real-time digital filter, because it is a discrete time function, works with digitized data as opposed to a continuous waveform, and a new data point is acquired each sampling period. Because of this discrete nature, data samples are referenced as numbers such as sample 1, sample 2, sample 3, etc. Figure 1 shows a low frequency signal containing higher frequency noise which must be filtered out. This waveform must be digitized with an ADC to produce samples x(n). These data values are fed to the digital filter, which in this case is a lowpass filter. The output data samples, y(n), are used to reconstruct an analog waveform using a low glitch DAC.Digital filters, however, are not the answer to all signal processing filtering requirements. In order to maintain real-time operation, the DSP processor must be able to execute all the steps in the filter routine within one sampling clock period1/f s.A fast general purpose fixed-point DSP such as the ADSP-2189M at 75MIPS can 。
IIR数字滤波器英文文献以及翻译
2013 届毕业设计（论文）英文文献及其翻译资料院、部：电气与信息工程学院学生姓名：指导教师：职称专业：电子信息工程班级：完成时间：2013年6月7日Signal processingSignal processing is an area of electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time, to perform useful operations on those signals. Signals of interest can include sound, images, time-varying measurement values and sensor data, for example biological data such as electrocardiograms, control system signals, telecommunication transmission signals such as radio signals, and many others. Signals are analog or digital electrical representations of time-varying or spatial-varying physical quantities. In the context of signal processing, arbitrary binary data streams and on-off signalling are not considered as signals, but only analog and digital signals that are representations of analog physical quantities.HistoryAccording to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. They further state that the "digitalization" or digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s.Categories of signal processingAnalog signal processingAnalog signal processing is for signals that have not been digitized, as in classical radio, telephone, radar, and television systems. This involves linear electronic circuits such as passive filters, active filters, additive mixers, integrators and delay lines. It also involves non-linear circuits such as compandors, multiplicators (frequency mixers and voltage-controlled amplifiers), voltage-controlled filters, voltage-controlled oscillators and phase-locked loops.Discrete time signal processingDiscrete time signal processing is for sampled signals that are considered as defined only at discrete points in time, and as such are quantized in time, but not in magnitude.Analog discrete-time signal processing is a technology based on electronic devices such as sample and hold circuits, analog time-division multiplexers, analog delay lines and analog feedback shift registers. This technology was a predecessor of digital signal processing (see below), and is still used in advanced processing of gigahertz signals.The concept of discrete-time signal processing also refers to a theoretical discipline that establishes a mathematical basis for digital signal processing, without taking quantization error into consideration.Digital signal processingDigital signal processing is for signals that have been digitized. Processing is done by general-purpose computers or by digital circuits such as ASICs, field-programmable gate arrays or specialized digital signal processors (DSP chips). Typical arithmetical operations include fixed-point and floating-point, real-valued and complex-valued, multiplication and addition. Other typical operations supported by the hardware are circular buffers and look-up tables. Examples of algorithms are the Fast Fourier transform (FFT), finite impulse response (FIR) filter, Infinite impulse response (IIR) filter, and adaptive filters such as the Wiener and Kalman filters1.Digital signal processingDigital signal processing (DSP) is concerned with the representation of signals by a sequence of numbers or symbols and the processing of these signals. Digital signal processing and analog signal processing are subfields of signal processing. DSP includes subfields like: audio and speech signal processing, sonar and radar signal processing, sensor array processing, spectral estimation, statistical signal processing, digital image processing, signal processing for communications, control of systems, biomedical signal processing, seismic data processing, etc.The goal of DSP is usually to measure, filter and/or compress continuous real-world analog signals. The first step is usually to convert the signal from an analog to a digital form, by sampling it using an analog-to-digital converter (ADC), which turns the analog signal into a stream of numbers. However, often, the required output signal is another analog output signal, which requires a digital-to-analogconverter (DAC). Even if this process is more complex than analog processing and has a discrete value range, the application of computational power to digital signal processing allows for many advantages over analog processing in many applications, such as error detection and correction in transmission as well as data compression.[1]DSP algorithms have long been run on standard computers, on specialized processors called digital signal processors (DSPs), or on purpose-built hardware such as application-specific integrated circuit (ASICs). Today there are additional technologies used for digital signal processing including more powerful general purpose microprocessors, field-programmable gate arrays (FPGAs), digital signal controllers (mostly for industrial apps such as motor control), and stream processors, among others.[2]2. DSP domainsIn DSP, engineers usually study digital signals in one of the following domains: time domain (one-dimensional signals), spatial domain (multidimensional signals), frequency domain, autocorrelation domain, and wavelet domains. They choose the domain in which to process a signal by making an informed guess (or by trying different possibilities) as to which domain best represents the essential characteristics of the signal. A sequence of samples from a measuring device produces a time or spatial domain representation, whereas a discrete Fourier transform produces the frequency domain information, that is the frequency spectrum. Autocorrelation is defined as the cross-correlation of the signal with itself over varying intervals of time or space.3. Signal samplingMain article: Sampling (signal processing)With the increasing use of computers the usage of and need for digital signal processing has increased. In order to use an analog signal on a computer it must be digitized with an analog-to-digital converter. Sampling is usually carried out in two stages, discretization and quantization. In the discretization stage, the space of signals is partitioned into equivalence classes and quantization is carried out by replacing the signal with representative signal of the corresponding equivalence class. In thequantization stage the representative signal values are approximated by values from a finite set.The Nyquist–Shannon sampling theorem states that a signal can be exactly reconstructed from its samples if the sampling frequency is greater than twice the highest frequency of the signal; but requires an infinite number of samples . In practice, the sampling frequency is often significantly more than twice that required by the signal's limited bandwidth.A digital-to-analog converter is used to convert the digital signal back to analog. The use of a digital computer is a key ingredient in digital control systems.4. Time and space domainsMain article: Time domainThe most common processing approach in the time or space domain is enhancement of the input signal through a method called filtering. Digital filtering generally consists of some linear transformation of a number of surrounding samples around the current sample of the input or output signal. There are various ways to characterize filters; for example:∙ A "linear" filter is a linear transformation of input samples; other filters are "non-linear". Linear filters satisfy the superposition condition, i.e. if an input is a weighted linear combination of different signals, the output is an equally weighted linear combination of the corresponding output signals.∙ A "causal" filter uses only previous samples of the input or output signals; while a "non-causal" filter uses future input samples. A non-causal filter can usually be changed into a causal filter by adding a delay to it.∙ A "time-invariant" filter has constant properties over time; other filters such as adaptive filters change in time.∙Some filters are "stable", others are "unstable". A stable filter produces an output that converges to a constant value with time, or remains bounded within a finite interval. An unstable filter can produce an output that grows without bounds, with bounded or even zero input.A "finite impulse response" (FIR) filter uses only the input signals, while an "infinite impulse response" filter (IIR) uses both the input signal and previous samples of the output signal. FIR filters are always stable, while IIR filters may be unstable.Filters can be represented by block diagrams which can then be used to derive a sample processing algorithm to implement the filter using hardware instructions. A filter may also be described as a difference equation, a collection of zeroes and poles or, if it is an FIR filter, an impulse response or step response.The output of a digital filter to any given input may be calculated by convolving the input signal with the impulse response.5. Frequency domainMain article: Frequency domainSignals are converted from time or space domain to the frequency domain usually through the Fourier transform. The Fourier transform converts the signal information to a magnitude and phase component of each frequency. Often the Fourier transform is converted to the power spectrum, which is the magnitude of each frequency component squared.The most common purpose for analysis of signals in the frequency domain is analysis of signal properties. The engineer can study the spectrum to determine which frequencies are present in the input signal and which are missing.In addition to frequency information, phase information is often needed. This can be obtained from the Fourier transform. With some applications, how the phase varies with frequency can be a significant consideration.Filtering, particularly in non-realtime work can also be achieved by converting to the frequency domain, applying the filter and then converting back to the time domain. This is a fast, O(n log n) operation, and can give essentially any filter shape including excellent approximations to brickwall filters.There are some commonly used frequency domain transformations. For example, the cepstrum converts a signal to the frequency domain through Fourier transform, takes the logarithm, then applies another Fourier transform. This emphasizes thefrequency components with smaller magnitude while retaining the order of magnitudes of frequency components.6. Z-domain analysisWhereas analog filters are usually analysed on the s-plane; digital filters are analysed on the z-plane or z-domain in terms of z-transforms.Most filters can be described in Z-domain (a complex number superset of the frequency domain) by their transfer functions. A filter may be analysed in the z-domain by its characteristic collection of zeroes and poles.7. ApplicationsThe main applications of DSP are audio signal processing, audio compression, digital image processing, video compression, speech processing, speech recognition, digital communications, RADAR, SONAR, seismology, and biomedicine. Specific examples are speech compression and transmission in digital mobile phones, room matching equalization of sound in Hifi and sound reinforcement applications, weather forecasting, economic forecasting, seismic data processing, analysis and control of industrial processes, computer-generated animations in movies, medical imaging such as CAT scans and MRI, MP3 compression, image manipulation, high fidelity loudspeaker crossovers and equalization, and audio effects for use with electric guitar amplifiers8. ImplementationDigital signal processing is often implemented using specialised microprocessors such as the DSP56000, the TMS320, or the SHARC. These often process data using fixed-point arithmetic, although some versions are available which use floating point arithmetic and are more powerful. For faster applications FPGAs[3]might be used. Beginning in 2007, multicore implementations of DSPs have started to emerge from companies including Freescale and Stream Processors, Inc. For faster applications with vast usage, ASICs might be designed specifically. For slow applications, a traditional slower processor such as a microcontroller may be adequate. Also a growing number of DSP applications are now being implemented on Embedded Systems using powerful PCs with a Multi-core processor.信号处理信号处理是电气工程和应用数学领域，在离散的或连续的时间域处理和分析信号，以对这些信号进行所需的有用的操作。
数字滤波器的仿真与实现_中英文翻译
英文原文The simulation and the realization of the digital filterWith the information age and the advent of the digital world, digital signal processing has become one of today's most important disciplines and door technology. Digital signal processing in communications, voice, images, automatic control, radar, military, aerospace, medical and household appliances, and many other fields widely applied. In the digital signal processing applications, the digital filter is important and has been widely applied.1、figures Unit on :Analog and digital filtersIn signal processing, the function of a filter is to remove unwanted parts of the signal, such as random noise, or to extract useful parts of the signal, such as the components lying within a certain frequency range.The following block diagram illustrates the basic idea.There are two main kinds of filter, analog and digital. They are quite different in their physical makeup and in how they work. An analog filter uses analog electronic circuits made up from components such as resistors, capacitors and op amps to produce the required filtering effect. Such filter circuits are widely used in such applications as noise reduction, video signal enhancement, graphic equalisers in hi-fi systems, and many other areas. There are well-established standard techniques for designing an analog filter circuit for a given requirement. At all stages, the signal being filtered is an electrical voltage or current which is the direct analogue of the physical quantity (e.g. a sound or video signal or transducer output) involved. A digital filter uses a digital processor to perform numerical calculations on sampled values of the signal. The processor may be a general-purpose computer such as a PC, or a specialised DSP (Digital Signal Processor) chip. The analog input signal must first be sampled and digitised using an ADC (analog to digital converter). The resulting binary numbers, representing successive sampled values of the input signal, are transferred to the processor,which carries out numerical calculations on them. These calculations typically involve multiplying the input values by constants and adding the products together. If necessary, the results of these calculations, which now represent sampled values of the filtered signal, are output through a DAC (digital to analog converter) to convert the signal back to analog form.Note that in a digital filter, the signal is represented by a sequence of numbers, rather than a voltage or current.The following diagram shows the basic setup of such a system.Unit refers to the input signals used to filter hardware or software. If the filter input, output signals are separated, they are bound to respond to the impact of the Unit is separated, such as digital filters filter definition. Digital filter function, which was to import sequences X transformation into export operations through a series Y.According to figures filter function 24-hour live response characteristics, digital filters can be divided into two, namely, unlimited long live long live the corresponding IIR filter and the limited response to FIR filters. IIR filters have the advantage of the digital filter design can use simulation results, and simulation filter design of a large number of tables may facilitate simple. It is the shortcomings of the nonlinear phase; Linear phase if required, will use the entire network phase-correction. Image processing and transmission of data collection is required with linear phase filters identity. And FIR linear phase digital filter to achieve, but an arbitrary margin characteristics. Impact from the digital filter response of the units can be divided into two broad categories : the impact of the limited response (FIR) filters, and unlimited number of shocks to (IIR) digital filters.FIR filters can be strictly linear phase, but because the system FIR filter function extremity fixed at the original point, it can only use the higher number of bands to achieve their high selectivity for the same filter design indicators FIR filter called band than a few high-IIR 5-10 times, the cost is higher, Signal delay is also larger. But if the same linear phase, IIR filters must be network-wide calibration phase, the same section also increase the number of filters and network complexity. FIR filters can be used to achieve non-Digui way, not in a limited precision of a shock, and into the homes and quantitative factors of uncertainty arising from the impact of errors than IIR filter small number, and FIR filter can be used FFT algorithms, the computational speed. But unlike IIR filter can filter through the simulation results, there is no ready-made formula FIR filter must use computer-aided design software (such as MATLAB) to calculate. So, a broader application of FIR filters, and IIR filters are not very strict requirements on occasions.Unit from sub-functions can be divided into the following four categories :(1) Low-filter (LPF);(2) high-filter (HPF);(3) belt-filter (BPF);(4) to prevent filter (BSF).The following chart dotted line for the ideals of the filter frequency characteristics :A1(f) A2(f)10 f2cf 0 f2cf(a) (b)A3(f) A4(f)0 f1c f2cf 0 f1cf2cf(c) (d)(a)LPF (b)HPF (c)BPF (d)BSF2、MATLAB introducedMATLAB is a matrix laboratory (Matrix Laboratory) is intended. In addition to an excellent value calculation capability, it also provides professional symbols terms, word processing, visualization modeling, simulation and real-time control functions. MATLAB as the world's top mathematical software applications, with a strong engineering computing, algorithms research, engineering drawings, applications development, data analysis and dynamic simulation, and other functions, in aerospace, mechanical manufacturing and construction fields playing an increasingly important role. And the C language function rich, the use of flexibility, high-efficiency goals procedures. High language both advantages as well as low level language features. Therefore, C language is the most widely used programming language. Although MATLAB is a complete, fully functional programming environment, but in some cases, data and procedures with the external environment of the world is very necessary and useful. Filter design using Matlab, could be adjusted with the design requirements and filter characteristics of the parameters, visual simple, greatly reducing the workload for the filter design optimization.In the electricity system protection and secondary computer control, many signal processing and analysis are based on are certain types Yeroskipou and the second harmonics of the system voltage and current signals (especially at D process), are mixed with a variety of complex components, the filter has been installed power system during the critical components. Current computer protection and the introduction of two digital signal processing software main filter. Digital filter design using traditional cumbersome formula, the need to change the parameters after recalculation, especially in high filters, filter design workload. Uses MATLAB signal processing boxes can achieve rapid and effective digital filter design and simulation.MATLAB is the basic unit of data matrix, with its directives Biaodashi mathematics, engineering, commonly used form is very similar, it is used to solve a problem than in MATLAB C, Fortran and other languages End precision much the same thing. The popular MATLAB 5.3/Simulink3.0 including hundreds of internal function with the main pack and 30types of tool kits (Toolbox). kits can be divided into functional tool kits and disciplines toolkit. MATLAB tool kit used to expand the functional symbols terms, visualization simulation modelling, word processing and real-time control functions. professional disciplines toolkit is a stronger tool kits, tool kits control, signal processing tool kit, tool kits, etc. belonging to such communicationsMATLAB users to open widely welcomed. In addition to the internal function, all the packages MATLAB tool kits are readable document and the document could be amended, modified or users through Yuanchengxu the construction of new procedures to prepare themselves for kits.3、Digital filter designDigital filter design of the basic requirementsDigital filter design must go through three steps :(1) Identification of indicators : In the design of a filter, there must be some indicators. These indicators should be determined on the basis of the application. In many practical applications, digital filters are often used to achieve the frequency operation. Therefore, indicators in the form of general jurisdiction given frequency range and phase response. Margins key indicators given in two ways. The first is absolute indicators. It provides a function to respond to the demands of the general application of FIR filter design. The second indicator is the relative indicators. Its value in the form of answers to decibels. In engineering practice, the most popular of such indicators. For phase response indicators forms, usually in the hope that the system with a linear phase frequency bands human. Using linear phase filter design with the following response to the indicators strengths：①it only contains a few algorithms, no plural operations；②there is delay distortion, only a fixed amount of delay; ③the filter length N (number of bands for N-1), the volume calculation for N/2 magnitude.(2) Model approach : Once identified indicators can use a previous study of the basic principles and relationships, a filter model to be closer to the target system.(3) Achieved : the results of the above two filters, usually by differential equations, system function or pulse response to describe. According to this description of hardware or software used to achieve it.4、Introduced FPGAProgrammable logic device is a generic logic can use a variety of chips, which is to achieve ASIC ASIC (Application Specific Integrated Circuit) semi-customized device, Its emergence and development of electronic systems designers use CAD tools to design their own laboratory in the ASIC device. Especially FPGA (Field Programmable Gate Array) generated and development, as a microprocessor, memory, the figures for electronic system design and set a new industry standard (that is based on standard product sales catalogue in the market to buy). Is a digital system for microprocessors, memories, FPGA or three standard building blocks constitute their integration direction.Digital circuit design using FPGA devices, can not only simplify the design process and can reduce the size and cost of the entire system, increasing system reliability. They do not need to spend the traditional sense a lot of time and effort required to create integrated circuits, to avoid the investment risk and become the fastest-growing industries of electronic devices group. Digital circuit design system FPGA devices using the following main advantages(1)Design flexibleUse FPGA devices may not in the standard series device logic functional limitations. And changes in system design and the use of logic in any one stage of the process, and only through the use of re-programming the FPGA device can be completed, the system design provides for great flexibility.(2) Increased functional densityFunctional density in a given space refers to the number of functional integration logic. Programmable logic chip components doors several high, a FPGA can replace several films, film scores or even hundreds of small-scale digital IC chip illustrated in the film. FPGA devices using the chip to use digital systems in small numbers, thus reducing the number of chips used to reduce the number of printed size and printed, and will ultimately lead to a reduction in the overall size of the system.(3) Improve reliabilityPrinting plates and reduce the number of chips, not only can reduce system size, but it greatly enhanced system reliability. A higher degree of integration than systems in many low-standard integration components for the design of the same system, with much higher reliability. FPGA device used to reduce the number of chips required to achieve the system in the number printed on the cord and joints are reduced, the reliability of the system can beimproved.(4) Shortening the design cycleAs FPGA devices and the programmable flexibility, use it to design a system for longer than traditional methods greatly shortened. FPGA device master degrees high, use printed circuit layout wiring simple. At the same time, success in the prototype design, the development of advanced tools, a high degree of automation, their logic is very simple changes quickly. Therefore, the use of FPGA devices can significantly shorten the design cycle system, and speed up the pace of product into the market, improving product competitiveness.(5) Work fastFPGA/CPLD devices work fast, generally can reach several original Hertz, far larger than the DSP device. At the same time, the use of FPGA devices, the system needed to achieve circuitclasses and small, and thus the pace of work of the entire system will be improved.(6) Increased system performance confidentialityMany FPGA devices have encryption functions in the system widely used FPGA devices can effectively prevent illegal copying products were others(7) To reduce costsFPGA device used to achieve digital system design, if only device itself into the price, sometimes you would not know it advantages, but there are many factors affecting the cost of the system, taken together, the cost advantages of using FPGA is obvious. First, the use of FPGA devices designed to facilitate change, shorten design cycles, reduce development costs for system development; Secondly, the size and FPGA devices allow automation needs plug-ins, reducing the manufacturing system to lower costs; Again, the use of FPGA devices can enhance system reliability, reduced maintenance workload, thereby lowering the cost of maintenance services for the system. In short, the use of FPGA devices for system design to save costs.FPGA design principles :FPGA design an important guiding principles : the balance and size and speed of exchange, the principles behind the design of the filter expression of a large number of certification.Here, "area" means a design exertion FPGA/CPLD logic resources of the FPGA can be used to the typical consumption (FF) and the search table (IUT) to measure more general measure can be used to design logic equivalence occupied by the door is measured. "pace"means stability operations in the chip design can achieve the highest frequency, the frequency of the time series design situation, and design to meet the clock cycle -- PADto pad, Clock Setup Time, Clock Hold Beijing, Clock-to-Output Delay, and other characteristics of many time series closely related. Area (area) and speed (speed) runs through the two targets FPGA design always is the ultimate design quality evaluation criteria. On the size and speed of the two basic concepts : balance of size and speed and size and speed of swap.One pair of size and speed is the unity of opposites contradictions body. Requirements for the design of a design while the smallest, highest frequency of operation is unrealistic. More scientific goal should be to meet the design requirements of the design time series (includes requirements for the design frequency) premise, the smallest chip area occupied. Or in the specified area, the design time series cushion greater frequency run higher. This fully embodies the goals of both size and speed balanced thinking. On the size and speed requirements should not be simply interpreted as raising the level and design engineers perfect sexual pursuit, and should recognize that they are products and the quality and cost of direct relevance. If time series cushion larger design, running relatively high frequency, that the design Jianzhuangxing stronger, more quality assurance system as a whole; On the other hand, the smaller size of consumption design is meant to achieve in chip unit more functional modules, the chip needs fewer, the entire system has been significantly reduced cost. As a contradiction of the two components, the size and speed is not the same status. In contrast, meet the timetables and work is more important for some frequency when both conflicts, the use of priority guidelines.Area and the exchange rate is an important FPGA design ideas. Theoretically, if a design time series cushion larger, can run much higher than the frequency design requirements, then we can through the use of functional modules to reduce the consumption of the entire chip design area, which is used for space savings advantages of speed; Conversely, if the design of a time series demanding, less than ordinary methods of design frequency then generally flow through the string and data conversion, parallel reproduction of operational module, designed to take on the whole "string and conversion" and operate in the export module to chip in the data "and string conversion" from the macro point of view the whole chip meets the requirements of processing speed, which is equivalent to the area of reproduction - rate increase.For example. Assuming that the digital signal processing system is 350Mb/s input data flow rate, and in FPGA design, data processing modules for maximum processing speed of150Mb/s, because the data throughput processing module failed to meet requirements, it is impossible to achieve directly in the FPGA. Such circumstances, they should use "area-velocity" thinking, at least three processing modules from the first data sets will be imported and converted, and then use these three modules parallel processing of data distribution, then the results "and string conversion," we have complete data rate requirements. We look at both ends of the processing modules, data rate is 350Mb/s, and in view of the internal FPGA, each sub-module handles the data rate is 150Mb/s, in fact, all the data throughput is dependent on three security modules parallel processing subsidiary completed, that is used by more chip area achieve high-speed processing through "the area of reproduction for processing speed enhancement" and achieved design.FPGA is the English abbreviation Field of Programmable Gate Array for the site programmable gate array, which is in Pal, Gal, Epld, programmable device basis to further develop the product. It is as ASIC (ASIC) in the field of a semi-customized circuit and the emergence of both a customized solution to the shortage circuit, but overcome the original programmable devices doors circuit few limited shortcomings.FPGA logic module array adopted home (Logic Cell Array), a new concept of internal logic modules may include CLB (Configurable Logic Block), export import module IOB (Input Output Block) and internal links (Interconnect) 3. FPGA basic features are :(1) Using FPGA ASIC design ASIC using FPGA circuits, the chip can be used,while users do not need to vote films production.(2) FPGA do other customized or semi-customized ASIC circuits throughout the Chinese specimen films.3) FPGA internal capability and rich I/O Yinjue.4) FPGA is the ASIC design cycle, the shortest circuit, the lowest development costs, risks among the smallest device5) FPGA using high-speed Chmos crafts, low consumption, with CMOS, TTL low-power compatibleIt can be said that the FPGA chip is for small-scale systems to improve system integration, reliability one of the bestCurrently FPGA many varieties, the Revenue software series, TI companies TPC series, the fiex ALTERA company seriesFPGA is stored in films from the internal RAM procedures for the establishment of the state of its work, therefore, need to programmed the internal Ram. Depending on the different configuration, users can use a different programming methodsPlus electricity, FPGA, EPROM chips will be read into the film, programming RAM中data, configuration is completed, FPGA into working order. Diaodian, FPGA resume into white films, the internal logic of relations disappear, FPGA to repeated use. FPGA's programming is dedicated FPGA programming tool, using generic EPROM, prom programming device can. When the need to modify functional FPGA, EPROM can only change is. Thus, with a FPGA, different programming data to produce different circuit functions. Therefore, the use of FPGA very flexible.There are a variety of FPGA model : the main model for a parallel FPGA plus a EPROM manner; From the model can support a number of films FPGA; serial prom programming model could be used serial prom FPGA programming FPGA; The external model can be engineered as microprocessors from its programming microprocessors.Verilog HDL is a hardware description language for the algorithm level, doors at the level of abstract level to switch-level digital system design modelling. Modelling of the target figure by the complexity of the system can be something simple doors and integrity of electronic digital systems. Digital system to the levels described, and in the same manner described in Hin-time series modelling.Verilog HDL language with the following description of capacity : design behaviour characteristics, design data flow characteristics, composition and structure designed to control and contain the transmission and waveform design a certification mechanism. All this with the use of a modelling language. In addition, Verilog HDL language programming language interface provided by the interface in simulation, design certification from the external design of the visit, including specific simulation control and operation.Verilog HDL language grammar is not only a definition, but the definition of each grammar structure are clear simulation, simulation exercises. Therefore, the use of such language to use Verilog simulation models prepared by a certification. From the C programming language, the language inherited multiple operating sites and structures. Verilog HDL provides modelling capacity expansion, many of the initial expansion would be difficult to understand. However, the core subsets of Verilog HDL language very easy to learn and use, which is sufficient formost modelling applications. Of course, the integrity of the hardware description language is the most complex chips from the integrity of the electronic systems described.historyVerilog HDL language initially in 1983 by Gateway Design Automation companies for product development simulator hardware modelling language. Then it is only a dedicated language. Since their simulation, simulation devices widely used products, Verilog HDL as a user-friendly and practical language for many designers gradually accepted. In an effort to increase the popularity of the language activities, Verilog HDL language in 1990 was a public area. Open Verilog International (OVI) is to promote the development of Verilog international organizations. 1992, decided to promote OVI OVI standards as IEEE Verilog standards. The effort will ultimately succeed, a IEEE1995 Verilog language standard, known as IEEE Std 1364-1995. Integrity standards in Verilog hardware description language reference manual contains a detailed description.Main capacity：Listed below are the main Verilog hardware description language ability*Basic logic gate, and, for example, or have embedded in the language and nand* Users of the original definition of the term (UDP), the flexibility. Users can be defined in the original language combinations logic original language, the original language of logic could also be time series* Switches class infrastructure models, such as the nmos and pmos also be embedded in the language* Hin-language structure designated for the cost of printing the design and trails Shi Shi and design time series checks.* Available three different ways to design or mixed mode modelling. These methods include : acts described ways - use process of structural modelling; Data flow approach - use of a modelling approach Fuzhi expression; Structured way - using examples of words to describe modular doors and modelling.* Verilog HDL has two types of data : data types and sequence data line network types. Line network types that the physical links between components and sequence types that abstract data storage components.* To describe the level design, the structure can be used to describe any level module example* Design size can be arbitrary; Language is design size (size) impose any restrictions* Verilog HDL is no longer the exclusive language of certain companies but IEEE standards.* And the machine can read Verilog language, it may as EDA tools and languages of the world between the designers* Verilog HDL language to describe capacity through the use of programming language interface (PLI) mechanism further expansion. PLI is to allow external functions of the visit Verilog module information, allowing designers and simulator world Licheng assembly* Design to be described at a number of levels, from the switch level, doors level, register transfer level (RTL) to the algorithm level, including the level of process and content* To use embedded switching level of the original language in class switch design integrity modelling* Same language can be used to generate simulated incentive and certification by the designated testing conditions, such as the value of imports of the designated*Verilog HDL simulation to monitor the implementation of certification, the certification process of implementing the simulation can be designed to monitor and demonstrate value. These values can be used to compare with the expectations that are not matched in the case of print news reports.* Acts described in the class, not only in the RTL level Verilog HDL design description, and to describe their level architecture design algorithm level behavioural description* Examples can use doors and modular structure of language in a class structure described* Verilog HDL mixed mode modelling capabilities in the design of a different design in each module can level modelling* Verilog HDL has built-in logic function, such as*Structure of high-level programming languages, such as conditions of expression, and the cycle of expression language, language can be used* To it and can display regular modelling* Provide a powerful document literacy* Language in the specific circumstances of non-certainty that in the simulator, different models can produce different results; For example, describing events in the standard sequence of events is not defined.5、In troduction of DSPToday, DSP is w idely used in the modern techno logy and it has been the key part of many p roducts and p layed more and mo re impo rtant ro le in our daily life.Recent ly, Northw estern Po lytechnica lUniversity Aviation Microelect ronic Center has comp leted the design of digital signal signal p rocesso r co re NDSP25, w h ich is aim ing at TM S320C25 digital signal p rocesso r of Texas Inst rument TM S320 series. By using top 2dow n design flow , NDSP25 is compat ible w ith inst ruct ion and interface t im ing of TM S320C25.Digital signal processors (DSP) is a fit for real-time digital signal processing for high-speed dedicated processors, the main variety used for real-time digital signal processing to achieve rapid algorithms. In today's digital age background, the DSP has become the communications, computer, and consumer electronics products, and other fields based device.Digital signal processors and digital signal processing is inseparably, we usually say "DSP" can also mean the digital signal processing (Digital Signal Processing), is that in this digital signal processors Lane. Digital signal processing is a cover many disciplines applied to many areas and disciplines, refers to the use of computers or specialized processing equipment, the signals in digital form for the collection, conversion, recovery, valuation, enhancement, compression, identification, processing, the signals are compliant form. Digital signal processors for digital signal processing devices, it is accompanied by a digital signal processing to produce. DSP development process is broadly divided into three phases : the 20th century to the 1970s theory that the 1980s and 1990s for the development of products. Before the emergence of the digital signal processing in the DSP can only rely on microprocessors (MPU) to complete. However, the advantage of lower high-speed real-time processing can not meet the requirements. Therefore, until the 1970s, a talent made based DSP theory and algorithms. With LSI technology development in 1982 was the first recipient of the world gave birth to the DSP chip. Years later, the second generation based on CMOS工艺DSP chips have emerged. The late 1980s, the advent of the third generation of DSP chips. DSP is the fastest-growing 1990s, there have been four successive five-generation and the generation DSP devices. After 20 years of development, the application of DSP products has been extended to people's learning, work and all aspects of life and gradually become electronics products determinants.。
数字滤波器文献翻译
文献翻译外文：Digital filterIn electronics, computer science and mathematics, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is an electronic circuit operating on continuous-time analog signals. An analog signal may be processed by a digital filter by first being digitized and represented as a sequence of numbers, then manipulated mathematically, and then reconstructed as a new analog signal (see digital signal processing). In an analog filter, the input signal is "directly" manipulated by the circuit.A digital filter system usually consists of an analog-to-digital converter to sample the input signal, followed by a microprocessor and some peripheral components such as memory to store data and filter coefficients etc. Finally a digital-to-analog converter to complete the output stage. Program Instructions (software) running on the microprocessor implement the digital filter by performing the necessary mathematical operations on the numbers received from the ADC. In some high performance applications, an FPGA or ASIC is used instead of a general purpose microprocessor, or a specialized DSP with specific paralleled architecture for expediting operations such as filtering.Digital filters may be more expensive than an equivalent analog filter due to their increased complexity, but they make practical many designs that are impractical or impossible as analog filters. Since digital filters use a sampling process and discrete-time processing, theyexperience latency (the difference in time between the input and the response), which is almost irrelevant in analog filters.Digital filters are commonplace and an essential element of everyday electronics such as radios, cellphones, and stereo receivers.Characterization of digital filtersA digital filter is characterized by its transfer function, or equivalently, its difference equation. Mathematical analysis of the transfer function can describe how it will respond to any input. As such, designing a filter consists of developing specifications appropriate to the problem (for example, a second-order low pass filter with a specific cut-off frequency), and then producing a transfer function which meets the specifications.The transfer function for a linear, time-invariant, digital filter can be expressed as a transfer function in the Z-domain; if it is causal, then it has the form:where the order of the filter is the greater of N or M. See Z-transform's LCCD equation for further discussion of this transfer function.This is the form for a recursive filter with both the inputs (Numerator) and outputs (Denominator), which typically leads to an IIR infinite impulse response behaviour, but if the denominator is made equal to unity i.e. no feedback, then this becomes an FIR or finite impulse response filter.Analysis techniquesA variety of mathematical techniques may be employed to analyze the behaviour of a given digital filter. Many of these analysis techniques may also be employed in designs, and often form the basis of a filter specification.Typically, one analyzes filters by calculating how the filter will respond to a simple input such as an impulse response. One can then extend this information to visualize the filter's response to more complex signals. Riemann spheres have been used, together with digital video, for this purpose.Impulse responseThe impulse response, often denoted h[k] or h k, is a measurement of how a filter will respond to the Kronecker delta function. For example, given a difference equation, one would set x0 = 1 and x k = 0 for and evaluate. The impulse response is a characterization of the filter's behaviour. Digital filters are typically considered in two categories: infinite impulse response (IIR) and finite impulse response (FIR). In the case of linear time-invariant FIR filters, the impulse response is exactly equal to the sequence of filter coefficients:IIR filters on the other hand are recursive, with the output depending on both current and previous inputs as well as previous outputs. The general form of the an IIR filter is thus:Plotting the impulse response will reveal how a filter will respond to a sudden, momentary disturbance.Difference equationIn discrete-time systems, the digital filter is often implemented by converting the transfer function to a linear constant-coefficient difference equation (LCCD) via the Z-transform. The discrete frequency-domain transfer function is written as the ratio of two polynomials. For example:This is expanded:and divided by the highest order of z:The coefficients of the denominator, a k, are the 'feed-backward' coefficients and the coefficients of the numerator are the 'feed-forward' coefficients, b k. The resultant linear difference equation is:or, for the example above:rearranging terms:then by taking the inverse z-transform:and finally, by solving for y[n]:This equation shows how to compute the next output sample, y[n], in terms of the past outputs, y[n−p], the present input, x[n], and the past inputs, x[n−p]. Applying the filter to an input in this form is equivalent to a Direct Form I or II realization, depending on the exact order of evaluation.Filter designMain article: Filter designThe design of digital filters is a deceptively complex topic.[1] Although filters are easily understood and calculated, the practical challenges of their design and implementation are significant and are the subject of much advanced research.There are two categories of digital filter: the recursive filter and the nonrecursive filter. These are often referred to as infinite impulseresponse (IIR) filters and finite impulse response (FIR) filters, respectively.[2]Filter realizationAfter a filter is designed, it must be realized by developing a signal flow diagram that describes the filter in terms of operations on sample sequences.A given transfer function may be realized in many ways. Consider how a simple expression such as ax+ bx+ c could be evaluated –one could also compute the equivalent x(a + b) + c. In the same way, all realizations may be seen as "factorizations" of the same transfer function, but different realizations will have different numerical properties. Specifically, some realizations are more efficient in terms of the number of operations or storage elements required for their implementation, and others provide advantages such as improved numerical stability and reduced round-off error. Some structures are better for fixed-point arithmetic and others may be better for floating-point arithmetic.Direct Form IA straightforward approach for IIR filter realization is Direct Form I, where the difference equation is evaluated directly. This form is practical for small filters, but may be inefficient and impractical (numerically unstable) for complex designs.[3] In general, this form requires 2N delay elements (for both input and output signals) for a filter of order N.Direct Form IIThe alternate Direct Form II only needs N delay units, where N is the order of the filter –potentially half as much as Direct Form I. This structure is obtained by reversing the order of the numerator and denominator sections of Direct Form I, since they are in fact two linear systems, and the commutativity property applies. Then, one will notice that there are two columns of delays (z− 1) that tap off the center net, and these can be combined since they are redundant, yielding the implementation as shown below.The disadvantage is that Direct Form II increases the possibility of arithmetic overflow for filters of high Q or resonance.[4]It has been shown that as Q increases, the round-off noise of both direct form topologies increases without bounds.[5]This is because, conceptually, the signal is first passed through an all-pole filter (which normally boosts gain at the resonant frequencies) before the result of that is saturated, then passed through an all-zero filter (which often attenuates much of what the all-pole half amplifies).Cascaded second-order sectionsA common strategy is to realize a higher-order (greater than 2) digital filter as a cascaded series of second-order "biquadratric" (or "biquad") sections[6] (see digital biquad filter). Advantages of this strategy is that the coefficient range is limited. Cascading direct form II sections result in N delay elements for filter order of N. Cascading direct form I sections result in N+2 delay elements since the delay elements of the input of any section (except the first section) are a redundant with the delay elements of the output of the preceding section.文献翻译译文：数字滤波在电子学、计算机科学和数学中，数位滤波器是在一个系统上执行一个采样，在离散时间上对信号进行的数学运算，以减少或增加这种信号的某些方面。
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江西理工大学应用科学学院毕业设计(论文)外文资料翻译系：信息工程系专业：通信工程班级：姓名学号：附件： 1.外文资料翻译译文；2.外文原文。
附件一：外文资料翻译译文数字滤波器的仿真与实现当今，数字信号处理技术正飞速发展，它不但自成一门学科，更是以不同形式影响和渗透到其他学科；它与国民经济息息相关，与国防建设紧密相连；它影响或改变着我们的生产、生活方式，因此受到人们的普遍关注。
数字化、智能化和网络化是当代信息技术发展的大趋势，而数字化是智能化和网络化的基础，实际生活中遇到的信号多种多样，例如广播信号、电视信号、雷达信号、通信信号、导航信号、射电天文信号、控制信号、气象信号、遥感遥测信号，等等。
上述信号大部分是模拟信号，也有小部分数字信号。
模拟信号是自变量的连续函数，自变量可以是一维的，也可以是二维或多维的。
大多数情况下一维模拟信号的自变量是时间，经过时间上的离散化（采样）和幅度上的离散化（量化），这类模拟信号便成为一维数字信号。
因此，数字信号实际上是用数字序列表示的信号，语音信号经采样和量化，得到的数字信号是一个一维离散的时间序列；而图像信号经采样和量化后，得到的数字信号是一个二维离散空间序列。
数字信号处理，就是用数值计算的方法对数字序列进行各种处理，把信号变换成符合需要的某种形式。
例如，对数字信号经过滤波以限制他的频带或滤除噪音和干扰，或将他们与其他信号进行分离；对信号进行频谱分析或功率谱分析以了解信号的频谱组成，进而对信号识别；对信号进行某种变换，使之更适合传输、存储和应用；对信号进行编码以达到数据压缩的目的，等等。
数字滤波技术是数字信号分析、处理技术的重要分支。
无论是信号的获取、传输，还是信号的处理和交换都离不开滤波技术，它对信号安全可靠和有效灵活地传输是至关重要的。
在所有的电子系统中，使用最多技术最复杂的要算数字滤波器了，数字滤波器的优劣直接决定产品的优劣。
在信号处理过程中，所处理的信号往往混有噪声，从接收到的信号中消除或减弱噪音是信号处理和传输中十分重要的问题。
根据有用信号和噪音的不同特性，提取有用信号的过程称为滤波，实现滤波的系统称为滤波器。
在近代电信设备和各类控制系统中，数字滤波器的应用极为广泛，这里只列举部分应用最成功的领域。
（1）语音处理语音处理是最早应用数字滤波器的领域之一，也是最早推动数字信号处理理论发展的领域之一。
该领域主要包括5个方面的内容：第一，语音信号分析。
即对语音信号的波形特征、统计特征、模型参数等进行分析计算；第二，语音合成。
即利用专用数字硬件或在通用计算机上运行软件来产生语音；第三，语音识别。
即用专用硬件或计算机识别人讲的话，或者识别说话的人；第四，语音增强。
即从噪音或干扰中提取被掩盖的语音信号。
第五，语音编码。
主要用于语音数据压缩，目前已经建立了一系列语音编码的国际标准，大量用于通信和语音处理。
近年来，这5个方面都取得可不少的研究成果，并且，在市场上已出现了一些相关的软件和硬件产品。
例如，盲人阅读器、哑人语音合成器、口授打印机、语音应答机，各种会说话的仪器和玩具，以及通信和视听产品大量使用的音频编码技术。
（2）图像处理数字滤波技术以成功地应用于静态图像和活动图像的恢复和增强、数据压缩、去噪音和干扰、图像识别以及层析X射线摄影，还成功地应用于雷达、声纳、超声波和红外信号的可见图像成像。
（3）通信在通信技术领域内，几乎没有一个分支不受到数字滤波技术的影响。
信源编码、信道编码、调制、多路复用、数据压缩以及自适应信道均衡等，都广泛应用数字滤波器，特别是在数字通信、网络通信、图像通信、多媒体通信等应用中，离开了数字滤波器，几乎寸步难行。
其中，被认为是通信技术未来发展方向的软件无线电技术，更是以数字滤波器为基础。
（4）电视数字电视取代模拟电视已是必然趋势。
高清晰度电视的普及指日可待，与之配套的视频光盘技术已经形成具有巨大市场的产业；可视电话和会议电视产品不断更新换代。
视频压缩和音频压缩技术所取得的成就和标准化工作，促成了电视领域产业的蓬勃发展，而数字滤波器及其相关技术是视频压缩和音频压缩技术的重要基础。
（5）雷达雷达信号占有的频带非常宽，数据传输速率也非常高，因而压缩数据量好降低数据传输速率是雷达信号数字处理面临的首要问题。
高速数字器件的出现促进了雷达信号处理技术的进步。
在现代雷达系统中，数字信号处理部分是不可或缺的，因为从信号的产生、滤波、加工到目标参数的估计和目标成像显示都离不开数字滤波器技术。
雷达信号的数字滤波器是当今十分活跃的研究领域之一。
（6）生物医学信号处理数字滤波器在医学中的应用日益广泛，如对脑电图和心电图的分析、层析X射线摄影的计算机辅助分析、胎儿心音的自适应检测等。
（7）其他领域数字滤波器的应用领域如此广泛，以至于想完全列举他们是根本不可能的，除了以上几个领域外，还有很多其他的应用领域。
例如，在军事上被大量应用于导航、制导、电子对抗、战场侦测；在电力系统中被应用于能源分布规划和自动检测；在环境保护中被应用于对空气和噪声干扰的自动检测；在经济领域中被应用于股票市场预测和经济效益分析，等等。
数字滤波器介绍：模拟和数字滤波器在信号处理、过滤功能是一个不排除部分信息,如随机噪音、提取有用的信号部分,如部分地势在一定的频率范围.有两大类型的过滤, 模拟以及数字。
他们是完全不同的物理结构,如何工作. 类比电子电路模拟用的过滤部分组成,例如由电阻、电容opamps和生产所需的过滤效果. 这种过滤器被广泛使用的电路减少噪音等方面的应用,提高视频信号、图像均衡的高科技传真系统等众多领域. 有完善的技术标准设计的模拟电路进行过滤特定要求. 在各个阶段,是一个信号,是电机电压和过滤,目前直接的物理模拟量(例如声音或视频信号和变频器生产)处理. 数码过滤用数字进行数值计算处理器的信号抽样值. 处理器的可能通用计算机等PC或专业发展计划图(数字信号处理器)芯片. 模拟信号必须先投入使用的取样和数码艺术发展局(模拟到数字转换器). 由此二元多,占抽样连续输入信号的价值,转移到处理器,进行数字计算. 这些计算通常涉及多方面的投入和增加产品价值的共同因素. 如有必要,这些计算结果,现在是抽样信号值的过滤,产出通过发展援助委员会(类比数位转换器来)信号转换回模拟形式。
滤波器是指用来对输入信号进行滤波的硬件或软件。
如果滤波器的输入、输出都是离散信号，则该滤波器的冲击响应也必然是离散的，这样的滤波器定义为数字滤波器。
数字滤波器的功能，就是把输入序列X通过一定的运算变换成输出序列Y。
根据数字滤波器冲激响应函数的时域特性，可将数字滤波器分为两种，即无限长冲激相应IIR 滤波器和有限长冲激响应FIR滤波器。
IIR数字滤波器的优点是可以利用模拟滤波器设计的结果，而模拟滤波器的设计有大量图表可查，方便简单。
它的缺点是相位的非线性；若需要线性相位，则要采用全通网络进行相位校正。
图象处理以及数据采集传输都要求滤波器具有线性相位特性。
而FIR数字滤波器可以实现线性相位，又可具有任意幅度特性。
从数字滤波器的单位冲击响应来看，可分为两大类：有限冲击响应（FIR）数字滤波器和无限冲击响应（IIR）数字滤波器。
FIR滤波器却可以得到严格的线性相位，然而由于FIR滤波器的系统函数的极点固定在原点，所以只能用较高的阶数来实现其高选择性，对于同样的滤波器设计指标，FIR滤波器所要求的阶数要比IIR高5至10倍，所以成本较高，信号延迟也较大。
但是如果要求相同的线性相位，则IIR 滤波器就必须加全通网络进行相位校正，同样也要增加滤波器网络的节数和复杂性。
FIR滤波器可以用非递归的方法实现，在有限精度下不会产生振荡，同时由于量化舍入以及系数的不确定性所引起的误差的影响要比IIR滤波器小的多，并且FIR滤波器可以采用FFT算法，运算速度快。
但是不象IIR滤波器可以借助模拟滤波器的成果，FIR滤波器没有现成的计算公式，必须要用计算机辅助设计软件（如MATLAB）来计算。
由此可知，FIR滤波器应用比较广，而IIR滤波器则用在相位要求不是很严格的场合。
滤波器从功能上分又可分为如下4类:(1)低通滤波器(LPF)；(2)高通滤波器(HPF )；(3)带通滤波器(BPF )；(4)带阻滤波器(BSF)。
理想滤波器的幅频特性下图虚线为：2、MATLAB介绍：MATLAB是矩阵实验室（Matrix Laboratory）之意。
除具备卓越的数值计算能力外，它还提供了专业水平的符号计算，文字处理，可视化建模仿真和实时控制等功能。
MATLAB作为世界顶尖的数学应用软件，以其强大的工程计算、算法研究、工程绘图、应用程序开发、数据分析和动态仿真等功能，在航空航天、机械制造和工程建筑等领域发挥着越来越重要的作用。
而C语言功能丰富，使用灵活方便，目标程序效率高。
既有高级语言的优点，又有低级语言的特点。
因此，C语言是目前应用最广的编程语言。
虽然MATLAB是一个完整的、功能齐全的编程环境，但在某些情况下，与外部环境的数据和程序的交互是非常必须而且有益的。
利用MATLAB设计滤波器，可以随时对比设计要求和滤波器特性调整参数，直观简便，极大的减轻了工作量，有利于滤波器设计的最优化。
在电力系统微机保护和二次控制中，很多信号的处理与分析都是基于正旋基波和某些整次谐波而进行的，而系统电压电流信号（尤其是故障瞬变过程）中混有各种复杂成分，所以滤波器一直是电力系统二次装置的关键部件。
目前微机保护和二次信号处理软件主要采用数字滤波器。
传统的数字滤波器设计使用繁琐的公式计算，改变参数后需要重新计算，在设计滤波器尤其是高阶滤波器时工作量很大。
利用MATLAB信号处理箱可以快速有效地实现数字滤波器的设计与仿真。
MATLAB的基本数据单位是矩阵，它的指令表达式与数学,工程中常用的形式十分相似,故用MATLAB来解算问题要比用C,FORTRAN等语言完相同的事情简捷得多.当前流行的MATLAB 5.3/Simulink3.0包括拥有数百个内部函数的主包和三十几种工具包(Toolbox)。
工具包又可以分为功能性工具包和学科工具包.功能工具包用来扩充MATLAB的符号计算,可视化建模仿真,文字处理及实时控制等功能.学科工具包是专业性比较强的工具包,控制工具包,信号处理工具包,通信工具包等都属于此类。
开放性使MATLAB广受用户欢迎.除内部函数外,所有MATLAB主包文件和各种工具包都是可读可修改的文件,用户通过对源程序的修改或加入自己编写程序构造新的专用工具包。
3、数字滤波器的设计数字滤波器设计的基本要求数字滤波器设计要经过三个步骤：（1）确定指标：在设计一个滤波器前，必须有一些指标。
这些指标要根据应用确定。
在很多实际应用中，数字滤波器常常被用来实现选频操作。