Show ur work Design a band pass FIR filter. Using Blackman window to design a FI

Question

Show ur work

Design a band pass FIR filter. Using Blackman window to design a FIR band pass filter with Fs=8192hz and cut off frequency Fc1=500Hz and Fc2=3500Hz. You choose the order 10 of the filter. Generate an M-file. Using the designed filter to filter a short period music. Using 'Load handel' to load the music. Use function 'sound' to play the music before and after filtered. Hear the difference. Plot the signal in frequency domain before and after passing through filter. Change the order to 50 and re-design the filter. Observe the change of magnitude response. See how many coefficients you get now.

Explanation / Answer

clc;

clear all;

N=input('Enter order of the reqd BP filter ');

tau=(N-1)/2;

n1=0:N-1;

wc1=pi/4;

wc2=2*pi/3;

syms w n;

h=exp(1i*w*(n-tau));

h=load('test.wav');

hd=(1/(2*pi))*(int(h,w,-wc2,-wc1)+int(h,w,wc1,wc2));

for i=1:N

if i-1==tau

hdn(i)=(wc2-wc1)/pi;

else

hdn(i)=subs(hd,n,i-1);

end

end

hdn=real(hdn);

% All Window

for i=1:N

hamm_win(i) = 0.54 - 0.46*cos(2*pi*(i-1)/(N-1));

hann_win(i) = 0.5*(1 - cos(2*pi*(i-1)/(N-1)));

rect_win(i) = 1;

blac_win(i) = 0.42 - 0.5*cos(2*pi*(i-1)/(N-1)) + 0.08*cos(4*pi*(i-1)/(N-1));

end

hamm_hpf=hdn.*hamm_win;

hann_hpf=hdn.*hann_win;

rect_hpf=hdn.*rect_win;

blac_hpf=hdn.*blac_win;

figure;

subplot(4,3,1);

plot(hamm_hpf);

title('');

subplot(4,3,2);

plot(fir1(N-1,[wc1/pi wc2/pi],hamming(N)));

title('Blackman Window - Computed BandPass FIR Filter, MATLAB Inbuilt FIR Filter & Magnitude Response ');

hamm_hpfmag=sum(hamm_hpf.*exp(-1i*w*n1));

subplot(4,3,3);

ezplot(abs(hamm_hpfmag),[-pi pi]);

title('');

subplot(4,3,4);

plot(hann_hpf);

title('');

subplot(4,3,5);

plot(fir1(N-1,[wc1/pi wc2/pi],hann(N)));

title('Blackman Window - Computed BandPass FIR Filter, MATLAB Inbuilt FIR Filter & Magnitude Response ');

hann_hpfmag=sum(hann_hpf.*exp(-1i*w*n1));

subplot(4,3,6);

ezplot(abs(hann_hpfmag),[-pi pi]);

title('');

subplot(4,3,7);

plot(rect_hpf);

title('');

subplot(4,3,8);

plot(fir1(N-1,[wc1/pi wc2/pi],rectwin(N)));

title('Rectangular Window - Computed BandPass FIR Filter, MATLAB Inbuilt FIR Filter & Magnitude Response ');

rect_hpfmag=sum(rect_hpf.*exp(-1i*w*n1));

subplot(4,3,9);

ezplot(abs(rect_hpfmag),[-pi pi]);

title('');

subplot(4,3,10);

plot(blac_hpf);

title('');

subplot(4,3,11);

plot(fir1(N-1,[wc1/pi wc2/pi],blackman(N)));

title('Blackman Window - Computed BandPass FIR Filter, MATLAB Inbuilt FIR Filter & Magnitude Response ');

blac_hpfmag=sum(blac_hpf.*exp(-1i*w*n1));

subplot(4,3,12);

ezplot(abs(blac_hpfmag),[-pi pi]);

title('');

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