Q1: Design a 9th order low-pass filter with cut-off ?? /2 using the Hanning wind

Question

Q1: Design a 9th order low-pass filter with cut-off ?? /2 using the Hanning window. a) Plot its frequency response. b) Express the Input/ Output relation. c) let ??[??]{ 0    ??or ??=0,1,2…..,10

{1 ??or ??=11,12,…..30 Calculate ??=????. Plot and comment on the shape of y.

Q2: Design a 9th order high-pass filter with cut-off ??/ 4 using the Hanning window. a) Plot the frequency response. b) Express the Input/ Output relation. c) let ??[??]={ 0    ??or ??=0,1,2…..,10

{1    ??or ??=11,12,…..30             Calculate ??=????. Plot and comment on the shape of y.

Explanation / Answer

clc;

clear all;

rp = input('Enter the passband ripple = ');

rs = input('Enter the stopband ripple = ');

fp = input('Enter the passband frequency = ');

fs = input('Enter the stopband frequency = ');

f = input('Enter the sampling frequency = ');

wp = 2*fp/f; ws = 2*fs/f;

num = -20*log10(sqrt(rp*rs))-13;

dem = 14.6*(fs-fp)/f;

n = ceil(num/dem);

n1 = n+1;

if (rem(n,2)~=0) n1 = n;

n = n-1;

end y = hanning(n1);

% low-pass filter b = fir1(n,wp,y);

[h,o] = freqz(b,1,256);

m = 20*log10(abs(h));

subplot(2,2,1); plot(o/pi,m);

title('Magnitude Response of LPF');

ylabel('Gain in dB ---->');

xlabel('Normalised Frequency ---->');

grid on;

% high-pass filter b = fir1(n,wp,'high',y);

[h,o] = freqz(b,1,256);

m = 20*log10(abs(h));

subplot(2,2,2);

plot(o/pi,m);

title('Magnitude Response of HPF');

ylabel('Gain in dB ---->');

xlabel('Normalised Frequency ---->');

grid on;

% band pass filter wn = [wp ws];

b = fir1(n,wn,y);

[h,o] = freqz(b,1,256);

m = 20*log10(abs(h));

subplot(2,2,3);

plot(o/pi,m);

title('Magnitude Response of BPF');

ylabel('Gain in dB ---->');

xlabel('Normalised Frequency ---->');

grid on;

% band stop filter b = fir1(n,wn,'stop',y);

[h,o] = freqz(b,1,256);

m = 20*log10(abs(h));

subplot(2,2,4);

plot(o/pi,m);

title('Magnitude Response of BSF');

ylabel('Gain in dB ---->');

xlabel('Normalised Frequency ---->');

grid on;

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