外文翻译---FIR数字滤波器的设计

FIR Digital Filter Design

In chapter 9 we considered the design of IIR digital filters. For such filters, it is also necessary to ensure that the derived transfer function G(z) is stable. On the other hand, in the case of FIR digital filter design,the stability is not a design issue as the transfer function is a polynomial in z -1 and is thus always guaranteed stable. In this chapter, we consider the FIR digital filter design problem.

Unlike the IIR digital filter design problem, it is always possible to design FIR digital filters with exact linear-phase. First ,we describe a popular approach to the design of FIR digital filters with linear-phase. We then consider the computer-aided design of linear-phase FIR digital filters. To this end, we restrict our discussion to the use of matlab in determining the transfer functions. Since the order of the FIR transfer function is usually much higher than that of an IIR transfer function meeting the same frequency response specifications, we outline two methods for the design of computationally efficient FIR digital filters requiring fewer multipliers than a direct form realization. Finally, we present a method of designing a minimum-phase FIR digital filter that leads to a transfer function with smaller group delay than that of a linear-phase equivalent. The minimum-phase FIR digital filter is thus attractive in applications where the linear-phase requirement is not an issue. 10.1 preliminary considerations

In this section,we first review some basic approaches to the design of FIR digital filters and the determination of the filter order to meet the prescribed specifications. 10.1.1 Basic Approaches to FIR Digital Filter Design

Unlike IIR digital filter design, FIR filter design does not have any connection 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. Recall a causal FIR transfer function H(z) of length N+1 is a polynomial in z -1 of degree N: ∑=-=

N

n n

z

n h z H 0

][)( (10.1)

The corresponding frequency response is given by ∑=-=

N

n n

j j e

n h e H 0

][)(ωω

(10.2)

It has been shown in section 5.3.1 that any finite duration sequence x[n] of length N+1 is completely characterized by N+1 samples of its discrete-time Fourier transform X ()

ωj e . As a result, the design of an FIR filter of length N+1 can be accomplished by finding either the impulse response sequence {h[n]} or N+1 samples of its frequency response H ()

ωj e . Also ,to ensure a linear-phase design, the condition ][][n N h n h -±=,

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 10.2. The second approach is treated in Problems 10.31 and 10.32. In section 10.3, we outline computer-based digital filter design methods. 10.1.2 Estimation of the Filter Order

After the type of the digital filter has selected, the next step in the filter design process is to estimate the