[PDF] [PDF] Chapter 4: Problem Solutions

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In the previous lecture we considered the polynomial fit as a case example of All these methods though are just examples of weighted moving average filters design an IIR filter without any reference to analogue designs, for example by

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(ii) Ability to design lowpass IIR filters according to predefined specifications based on The idea is simply to sample impulse response of the analog filter to obtain the digital there is no aliasing problem as in the impulse invariance method

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design IIR filters get their name because their impulse response extends for Example: Compare the 7th-order Butterworth filter from previous examples with a

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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

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