Question

FIlters run the gamut. Let us consider two cases. (a) Butterworth: Smooth & Creamy? Design a high pass, Butterworth filter with a stopband stopping at 0.3n rads/sample, a passband starting at 0.5 rads/sample, and a minimum rise of 60dB 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 -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, cheblord, cheblap, and cheby2] (c) What would happen to the minimum order of the Chebyshev filter if the minimum rise between the stopband and passband was changed to 30 dB? Or 90 dB? Please generalize and explain how the minimum rise relates to filter order for this case.

Answer 1

wp=.4*pi;
ws=.6*pi
Rp=10;
Rs=60;
Wp = wp/500000; Ws = ws/500000;
%for butterworth
[n,Wn] = buttord(Wp,Ws,Rp,Rs);
[b,a] = butter(n,Wn,'low');
figure(1);zplane(b,a);
grid
title('pole zero plot for butterworth filter ');
disp('order of the butterworth filter=' );
disp(n);
%for chebyshev
[n,Wn] = cheb1ord(Wp,Ws,Rp,Rs);
[b,a]=cheby1(n,Rp,Wn,'low');
figure(2);zplane(b,a);
grid
title('pole zero plot for butterworth filter chebyshev filter');
disp('order of the chebyshev filter=' );
disp(n);

A MATLAB R2013a Figure 2 Figure 1 File Edit View Insert Tools Desktop Window Help File Edit View Insert Tools Desktop Window Help pole zero plot for butterworth filter chebyshev filter pole zero plot for butterworth filter Current Fol 0.8 0.6 0.4 0.2 0.8 0.6 0.4 10 60 3. 0000,-3. 01 E -0.2 0.4 0.6 -0.8 0.4 Icdat Icdat l Icdat 0.5 0.5 0.5 0.5 Real Part Real Part util audiowrite ( handel fdf. war' ,」 %-- 20-04-2017 09:30 --% order of the butterworth filter- randi (1 5],1,10) %-- 20-04-2017 18:48 --% %-- 20-04-2017 22:26 --% %-- 21-04-2017 20:31 --% 15 order of the chebyshev filter- buttche filter Details 20:48 ..1111, 21-04-2017

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