Filter design using frequency sampling Design a low pass fil

Filter design using frequency sampling. Design a low pass filter with a cut - off frequency omega_c = Pi/4. Generate the plots for the filter coefficients for filter lengths N = 21 and N = 41. Design a low pass filter with a cut - off frequency omega_c = 3 pi/8. Generate the plots for filter lengths N = 21 and N = 41. Turn in the Plots for cases above and just the code for the last part.

Solution

a)The following MATLAB code was used:
n=-20:20;
wc=0.25*pi;
h = (wc/pi)*sinc(wc/pi*n);
hprime = h.*hamming(21)’;
% All done - no need to shift - just interpret hprime as the shifted
% impulse response.
% Plot the frequency response:
freqz(hprime,1)

The following MATLAB code was used:
n=-20:20;
wc=0.25*pi;
h = (wc/pi)*sinc(wc/pi*n);
hprime = h.*hamming(41)’;
% All done - no need to shift - just interpret hprime as the shifted
% impulse response.
% Plot the frequency response:
freqz(hprime,1)

b)The following MATLAB code was used:
n=-20:20;
wc=0.375*pi;
h = (wc/pi)*sinc(wc/pi*n);
hprime = h.*hamming(21)’;
% All done - no need to shift - just interpret hprime as the shifted
% impulse response.
% Plot the frequency response:
freqz(hprime,1)

The following MATLAB code was used:
n=-20:20;
wc=0.375*pi;
h = (wc/pi)*sinc(wc/pi*n);
hprime = h.*hamming(41)’;
% All done - no need to shift - just interpret hprime as the shifted
% impulse response.
% Plot the frequency response:
freqz(hprime,1)