hw7slns - Homework#7Solutions

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Homework #7 Solutions For the Butterworth filter, we can use equation (10.3.46) and perform the bilinear transformation on s to get the frequency response for our digital filter. The code and plots are below. Matlab code: %problem 10.15 T = 1/24000; %sampling frequency (seconds) omega = 0:pi/100:pi; %digital filter plotting range Omega = 0:pi/100:pi; %analog filter plotting range WpOrig = 4000; WsOrig = 6000; wp = 2*T*WpOrig*pi; %digital passband frequency (radians) ws = 2*T*WsOrig*pi; %digital stopband frequency (radians)
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Rp = 1; %passband ripple Rs = 40; %stopband attenuation %Analog filter with prewarping Wp = 2*tan(wp/2); %analog passband frequency (rad/s) (with prewarping) Ws = 2*tan(ws/2); %analog stopband frequency (rad/s) (with prewarping) %MATLAB function specifications [N, WpButter] = buttord(Wp,Ws,Rp,Rs, 's' ); [Bbutter, Abutter] = butter(N,WpButter, 's' ); [BdButter, AdButter] = bilinear(Bbutter,Abutter,1); HdButter = freqz(BdButter,AdButter,omega); %frequency response %Our specifications
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hw7slns - Homework#7Solutions

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