Chapter 4: Problem Solutions




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Chapter 4: Problem Solutions

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Chapter 4: Problem Solutions 96_6Solutions_Chapter4[1].pdf

Chapter 4: Problem Solutions

Digital Filters

Problems on Non Ideal Filters

Problem 4.1

We want to design a Discrete Time Low Pass Filter for a voice signal. The specifications are:

Passband F

p

4kHz, with 0.8dB ripple;

Stopband F

S

4.5kHz, with 50dB attenuation;

Sampling Frequency F

s

22kHz.

Determine a) the discrete time Passband and Stopband frequencies, b) the maximum and minimum values of H in the Passband and the Stopband, where H is the filter frequency response.Solution a) Recall the mapping from analog to digital frequency 2SFF s , with F s the sampling fre- quency. Then the passband and stopband frequencies become p 2422 rad0.36rad, s

24.522 rad0.41rad;

b) A 0.8dB ripple means that the frequency response in the passband is within the interval 1 where is such that 20 log 10

10.8 This yields 10

0.04

1 0.096. Therefore the

frequency response within the passband is within the interval

0.9035H+1.096.

Similarly in the stopband the maximum value is

H+10 5020
0.0031

Problem 4.2

A Digital Filter has frequency response

H such that

0.95H1.05 for 00.3 0

H
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