Digital signal processing-05

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What is DSP?

The analog waveform is sliced into equal segments and the waveform amplitude is measured in the middle of each segment The collection of measurements make up p the digital representation of the waveform
Where x[n] = xa(nT) are the ideal samples of xa(t) and h0(t) is the impulse response of the zero-order-hold system, namely,

The A/D converter is a physical device that converts a voltage or current amplitude at its input into a binary code representing a quantized amplitude value closest to the amplitude of the input. input .

Thus, it is desirable to eliminate the CT filters or simplify the requirement on them.

Sharp-cutoff filters are difficult and expensive Sharpto implement in DT DT. .



Under the control of an external clock( clock(外部时钟), the A/D converter can be caused to start and complete an A/D conversion every T seconds seconds. . However, the conversion is not instantaneous, and for this reason, a high high-performance A/D system typically includes a samplesample -andand-hold. Output of an ideal sample sample-andand-hold system i is

Thus, for an ideal lowpass antialiasing filter, the system behaves as a LTI system even when Xc(jΩ) is not bandlimited. bandlimited. In practice, the Haa(jΩ) can not be ideally bandlimited, but Haa(jΩ) can be made very small for bandlimited, |Ω|>π/T so that aliasing is minimized. minimized. Therefore, the overall system will be approximately

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2011/11/17
AnalogAnalog -to to-Digital (A/D) Conversion
Discrete-time system
y[n]

Low pass prefiltering to avoid aliasing


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Cont’

The abovementioned situation can be accomplished by lowpass filtering to CT signal prior to C/D conversion. conversion.

要求： sharp sharp-cutoff antialiasing filter. filter. 有源网络和集成电路(IC)可以实现. 数字信号处理中：a major part of the cost of a system for DT processing of analog signals. signals.


How Does It Work?

Faithful Duplication Resolution Trade Trade-offs
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State Key Laboratory of Mechanical System & Vibration

An ideal C/D converter converts a CT signal into a DT signal, precision. . where each sample is known with infinite precision Digital signal processing is an approximation to this, which converts a CT (analog) signal into a digital signal, i.e., a sequence of finitefinite-precision or quantized samples samples. .
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xc(t)
Anti-aliasing filter
Sample
A/D
xa(t) and hold x0(t) converter x[n]
Because of the conversion is not instantaneous
2011/11/17
Shanghai Jiao Tong University
Overview What is DSP? Converting Analog into Digital
Electronically Computationally C i ll


工程信号处理与应用
采样Leabharlann BaiduSchool of Mechanical Engineering fcli@sjtu.edu.cn
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Digital Processing of Analog Signals

Prefiltering to Avoid Aliasing
模拟信号处理， 模拟信号处理 ，期望: minimize sampling rate. If the input is not bandlimited or if the Nyquist frequency of the input is too high, prefiltering may be necessary. necessary. Example: Speech signal Example: signal: : only lowlow-frequency band up to 3-4kHz is required for intelligibility; intelligibility; the real speech signal may have significant frequency content in the 4kHz to 20kHz 20kHz range. range. For naturally bandlimited signal, wideband additive noise may fill in the higher frequency range, and in sampling, these noise components would be aliased into the low low-frequency band band. . If we wish to avoid aliasing, the input signal must be forced to be bandlimited. bandlimited.
What is DSP

What is DSP?
Converting a continuously changing waveform (analog) into a series of discrete levels (digital)
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State Key Laboratory of Mechanical System & Vibration

Therefore,
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The ideal sample sample-andand-hold is equivalent to impulse train modulation followed by linear filtering with the zerozero-orderorderhold system (零阶保持系统的线性滤波).


Ideally, the frequency response of the antialiasing filtering would be

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State Key Laboratory of Mechanical System & Vibration


The ideal C/D converter represents sampling performed sample-and and-hold and the quantizer and coder together by sample represent the operation of A/D converter converter. . The quantizer is a nonlinear system whose purpose is to transform the input sample x[n] into one of a finite set of prescribed values values. .
Specifically, the output of the zero-order-hold is a staircase waveform p values where the sample are held constant during the sampling period of T seconds. The purpose of this is to provide the constant input voltage (or current) required by the A/D converter.