Transcription of Chapter 4: Problem Solutions
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Chapter 4: Problem Solutions
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 freq
the impulse response of a FIR filter which approximates this frequency response. Plot the frequency response in terms of magnitude and phase to verify that the approximation holds. Solution In the digital domain, let 2 F Fs and therefore F Fs 2 . Therefore the filter's desired frequency response becomes H
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