Transcription of Chapter 4: Problem Solutions - Naval Postgraduate School
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Chapter 4: Problem Solutions - Naval Postgraduate School
Chapter 4: Problem SolutionsDigital FiltersProblems on Non Ideal Filters Problem want to design a Discrete Time Low Pass Filter for a voice signal. The specifications are:Passband Fp 4 kHz, with dB ripple;Stopband FS kHz, with 50dB attenuation;Sampling Frequency Fs 22 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 ) Recall the mapping from analog to digital frequency 2 F Fs, with Fs the sampling fre-quency. Then the passband and stopband frequencies become p 2 4 22 rad rad, s 2 22 rad rad;b) A dB ripple means that the frequency response in the passband is within the interval 1 where is such that 20 log10 1 This yields 1 Therefore the frequency response within the passband is within the interval H Similarly in the stopband the maximum value is H 10 50 20 Problem Digital Filter has frequency response H such that H for 0 0 H for Also let the sampling frequency be Fs 8 kHz.
0.5842 A 21 0.4 .07886 A 21 4.53 N A 8 2.285 257.434 which yields a window of length N 259 and a time delay L 129. Finally thr impulse response becomes h n hd n 129 wkaiser n àProblem 4.11 You want to design a low pass filter with passband Fp 2
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