Notes

Exp 6

clc;
clear all;
close all;
w=input('Enter the cut off freq');
N=input('No. of samples');
wc= 2*pi*w;
alpha= (N-1)/2;
eps= 0.001;
for n= 0:1:N-1
hd(n+1)=sin(-wc*(n-alpha+eps))/(pi*(n-alpha+eps));
end
wr=ones(1,N);
hn=hd.*wr;
w=0:0.01:pi;
h=freqz(hn,1,w);
subplot(1,3,1);
plot(w/pi,abs(h),'b');
grid;
xlabel('Nnormalised Freq');
ylabel('Mag');
title('angle');
subplot(1,3,2);
plot(w/pi,angle(h),'g');
grid;
xlabel('Normalised Freq');
ylabel('Mag');
title('angle');
subplot(1,3,3);
plot(w/pi,20*log10(h),'r');
grid;
xlabel('N normalised Freq');
ylabel('Log Mag');
title('Log Mag');



Exp 7


clc;
clear all;
close all;
wc=0.2*pi;
N=7;
hd=zeros(1,N);
A=(N-1)/2;
hna=wc/pi;
K=1:1:((N-1)/2);
n=K-1-((N-1)/2);
hd(K)=(sin(wc*n))/(pi*n);
hn(K)=hd(K);
hn=[hn,hna];
a=(N-1)/2;
w=0:pi/16:pi;
Hw1=hna*exp(-1j*w*a);
Hw2=0;
for m=1:1:a;
Hw3=hn(m)*((exp(1j*w*(1-m))+(exp(-1j*w*(1-m+2*a)))));
Hw2=Hw2+Hw3;
end
Hw=Hw2+Hw1;
H_mag=abs(Hw);
plot(w/pi,H_mag,'K');
grid;
title('Mag Resp');
xlabel('Normalised Freq');
ylabel('Mag');


Exp 7

clc;
clear all;
close all;
wc=0.2*pi;
N=7;
hd=zeros(1,N);
A=(N-1)/2;
hna=wc/pi;
K=1:1:((N-1)/2);
n=K-1-((N-1)/2);
hd(K)=(sin(wc*n))/(pi*n);
hn(K)=hd(K);
hn=[hn,hna];
a=(N-1)/2;
w=0:pi/16:pi;
Hw1=hna*exp(-1j*w*a);
Hw2=0;
for m=1:1:a;
Hw3=hn(m)*((exp(1j*w*(1-m))+(exp(-1j*w*(1-m+2*a)))));
Hw2=Hw2+Hw3;
end
Hw=Hw2+Hw1;
H_mag=abs(Hw);
plot(w/pi,H_mag,'K');
grid;
title('Mag Resp');
xlabel('Normalised Freq');
ylabel('Mag');


Exp 8


clc;
clear all;
close all;
x=input('Enter the x(n): ');
h=input('Enter the h(n): ');
n1=length(x);
n2=length(h);
N=n1+n2-1;
y=zeros(1,N);
h1=[h zeros(1,n2-1)];
n3= length(h1);
y= zeros(1,N+n3-n2);
H= fft(h1);
for i= 1:n2:n1
if 1<=(n1+n2-1);
X1=[x(1:1+n3-n2),zeros(1,n3-n2)];
else
X1=[x(1:n1),zeros(1,n3-n3)];
end
X2= fft(X1);
X3= X2.*H;
X4= round(ifft(X3));
if (i==1);
y(i:i+n3-1)=y(i:i+n3-1)+X4(1:n3);
end
end
disp('The o/p sequence y(n): ');
disp(y(1:N));
stem(y(1:N));
title('Overlap add method');
xlabel('n');
ylabel('y(n)');

Exp 9


clc;
close all;
x= input('x= ');
h=input('h= ');
L=input('L= ');
N1=length(x);
M=length(h);
lc=conv(x,h);
x=[x zeros(1,mod(-N1,L)) zeros(1,L)];
N2=length(x);
h= [h zeros(1,L-1)];
H= fft(h ,L+M-1);
s= N2/L;
index= 1:L;
xm=x(index);
x1=[zeros(1,M-1) xm];
X= [];
for stage = 1:s
X1=fft(x1,L+M-1);
Y=X1.*H;
Y=ifft(Y);
index2=M:M+L-1;
Y=Y(index2);
X=[X Y];
index3=(((stage)*L)-M+2):((stage+1)*L)
if index3(L+M-1)<=N2;
x1=x(index3);
end
end
i= 1:N1+M-1;
x=x(i);
similarity=corrcoef(x,lc);
figure
subplot(2,1,1);
stem(lc);
title('Conv using Conv() Func ');
xlabel('n');
ylabel('y(n)');
subplot(2,1,2);
stem(x);
title('Conv using Overlap Save Method ');
xlabel('n');
ylabel('y(n)');

Sub

clc;
clear all;
x = input('Enter the sequence x(n) = ');
h = input('Enter the sequence h(n) = ');
n1 = length(x);
n2 = length(h);
N = n1+n2-1;
h1 = [h zeros(1,N-n1)];
n3 = length(h1);
y = zeros(1,N);
x1 = [zeros(1,n3-n2) x zeros(1,n3)];
H = fft(h1);
for i = 1:n2:N
y1 = x1(i:i+(2*(n3-n2)));
y2 = fft(y1);
y3 = y2.*H;
y4 = round(ifft(y3));
y(i:(i+n3-n2)) = y4(n2:n3);
end
subplot(3,1,1);
stem(x(1:n1));
grid on;
title('Input Sequence x(n)');
xlabel('Time --->');
ylabel('Amplitude --->');
subplot(3,1,2);
stem(h(1:n2));
grid on;
title('Input Sequence h(n)');
xlabel('Time --->');
ylabel('Amplitude --->');
subplot(3,1,3);
disp(' Convolution Using Overlap Save Method = ');
disp(y(1:N));
stem(y(1:N));
grid on;
title(' Convolution Using Overlap Save Method');
xlabel('Time --->');
ylabel('Amplitude --->');