The MATLAB signal processing toolbox function butter helps design analog Butter-

Question

The MATLAB signal processing toolbox function butter helps design analog Butter-worth filters. Use MATLAB help to learn how butter works. For each of the following cases, design the filter, plot the filter's poles and zeros in the complex s plane, and plot the decibel magnitude response 20 log_10 |H(j omega)|. a. Design a sixth-order analog lowpass filter with omega_c = 2 pi 3500. b. Design a sixth-order analog highpass filter with omega_c = 2 pi 3500. c. Design a sixth-order analog bandpass filter with a passband between 2 and 4 kHz. d. Design a sixth-order analog bandstop filter with a stopband between 2 and 4 kHz.

Explanation / Answer

complete step by step matlab code for the following filter designs for sampling frequency of 1000and 500

a)
fc = 3500;
fs = 1000;

[b,a] = butter(6,fc/(fs/2));
freqz(b,a)

b)
[z,p,k] = butter(6,3500/500,'high');
sos = zp2sos(z,p,k);
fvtool(sos,'Analysis','freq')
c)
[A,B,C,D] = butter(6,[2000 4000]/500);
d = designfilt('bandpassiir','FilterOrder',6, ...
'HalfPowerFrequency1',2000,'HalfPowerFrequency2',4000, ...
'SampleRate',500);
sos = ss2sos(A,B,C,D);
fvt = fvtool(sos,d,'Fs',500);
legend(fvt,'butter','designfilt')

d)

[b,a] = butter(6,[0.2 0.4],'stop');
freqz(b,a)

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