Design Filter Filters run the gamut. Let us consider two cases. (a) Butterworth:
ID: 2081728 • Letter: D
Question
Design Filter
Filters run the gamut. Let us consider two cases. (a) Butterworth: Smooth & Creamy? Design a low pass, Butterworth filter with a passband finishing at 0.4 pi rads/sample, a stopband which starts at 0.6 pi rads/sample, and a minimum drop of 50dB between them. What is the lowest order filter you can have which satisfies these criterion? Please plot the poles and zeros of this filter in the z-plane. [See Also: Matlab functions: buttord, butter, bode, tf, zplane, and freqz] (b) Chebyshev: Sharp, but Rough? Please now design a Chebyshev filter to the same specifications. What's the lowest order it can take, while satisfying the criterion? Please justify your choice of Chebyshev filter. [See Also: The Matlab functions: cheby1, cheb1ord, cheb1ap, and cheby2]Explanation / Answer
a.) Wp = 40/50; Ws = 60/50; [n,Wn] = buttord(Wp,Ws,3,60) [z,p,k] = butter(n,Wn); sos = zp2sos(z,p,k); freqz(sos,512,1000) title(sprintf('n = %d Butterworth Lowpass Filter',n)) Wp = [100 200]/500; Ws = [50 250]/500; Rp = 3; Rs = 40; [n,Wn] = buttord(Wp,Ws,Rp,Rs) [z,p,k] = butter(n,Wn); sos = zp2sos(z,p,k); freqz(sos,128,1000) title(sprintf('n = %d Butterworth Bandpass Filter',n))