数字信号处理(第二版)(英文版) (7)

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Understanding DSP, Second Edition
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• Notice that the sudden changes in our input sequence of cars/minute are flattened out by our averager, just like passing an low-pass filter
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• In the case of averaging, y(n)th output is given by
• Write in a more general way
• For a general N-tap FIR filter, the nth output is
Understanding DSP, Second Edition
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Convolution of filter coefficients and the filter’s output impulse response
Understanding DSP, Second Edition
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• If we take a DFT transform of h(k) and x(n), we can get the following expression
• Relationships of convolution as applied to FIR digital filters
Understanding DSP, Second Edition
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Conclusion through the example of averaging
• FIR filters perform time-domain convolution by summing the products of the shifted input samples and a sequence of filter coefficients
Count the number of cars that pass over a bridge every minute, and then average number of cars per minute over five-minute intervals
Understanding DSP, Second Edition
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Outline
§7.1 An Introduction to Finite Impulse Response Filters(FIR)
§7.2 Properties of FIR Filters §7.3 Low-Pass FIR Filter Design §7.4 Examples to Design Other Types Linear
• an FIR filter’s output sequence is equal to the convolution of the input sequence and a filter’s impulse response (coefficients)
Understanding DSP, Second Edition
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§ 7.2 Properties of FIR Filters
7.2.1 Convolution in FIR Filters 7.2.2 Linear Phase FIR Filter 7.2.3 Linear Phase FIR Filter Structure 7.2.4 FIR Filter Poles and Zeros
Chapter 7 Design of FIR Digital Filter
let’s get started by illustrating the concept of filtering a time-domain signal as shown in Figure 7-1
Understanding DSP, Second Edition
• In the general case, if the kth input sample is x(k), then the nth output is
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Understanding DSP, Second Edition
Phase FIR Filter
Understanding DSP, Second Editห้องสมุดไป่ตู้on
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§ 7.1 An Introduction to FIR Filters
• FIR digital filters use only current and past input samples to obtain a current output sample value
Understanding DSP, Second Edition
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§ 7.2.1 Convolution in FIR Filters
Understand the case in a formal way--Averaging filter convolution
Understanding DSP, Second Edition
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• Formalize the digital filter nature of our averager by creating the block diagram as follow
Understanding DSP, Second Edition
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We can see the alternate averaging filter structure shown as follow:
• FIR Filters calculate the outputs in a manner much the same as processing of averaging
Understanding DSP, Second Edition
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Example For FIR------Averaging