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.
Passband Fp 4 kHz, with 0.8 dB ripple; Stopband FS 4.5 kHz, with 50dB attenuation; Sampling Frequency Fs 22 kHz. 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
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