Notes

Exp 2


clc
clear all
N=64;
x=randi(10,N,1)+i.*randi(10,N,1);
tic
W_N=exp(-2*1j*pi/N);
for i=1:N
for j=1:N
V_N(i,j)=W_N.^((i-1)*(j-1));
end
end
disp('The twiddle factor matrix')
V_N
x= V_N*x;
time(2)=toc;
V_real=real(V_N);
V_imaginary=imag(V_N);
subplot(2,2,1)
imshow(V_real);
title('Real parts of twiddle factor matrix as image')
subplot(2,1,2)
imshow(V_imaginary);
title('Imaginary parts of twiddle factor matrix as image')
tic
X_direct2=fft(x,N);
time_fft(2)=toc;



Exp 3

clc;
clear all;
close all;
x1=[1 1 1];
x2=[1 3 4 7];
N1=size(x1,2);
N2=size(x2,2);
N=max(N1,N2);
disp('Circular Convolution of result')
c=cconv(x1,x2,N)
N=5000;
x1=randi(10,N,1)+1i.*randi(10,N,1);
x2=randi(10,N,1)+1i.*randi(10,N,1);
x2c = conj(x2);
disp('Left hand side of Parsevels Theorem')
lhs=sum(x1.*x2c);
X1=fft(x1);
X2=fft(x2);
X2c=conj(X2);
disp('Right hand side of Parsevels Theorem')
rhs=(1/N).*sum(X1.*X2c);


exp 4

clc;
clear all;
close all;
x1=input('Enter the first sequence x1(n) = ');
x2=input('Enter the second sequence x2(n) = ');
L=length(x1);
M=length(x2);
N=L+M-1;
yn=conv(x1,x2);
disp('The values of yn are= ');
disp(yn);

n1=0:L-1;
subplot(3,1,1);
stem(n1,x1);
grid on;
xlabel('n1');
ylabel('amplitude');
title('First sequence');

n2=0:M-1;
subplot(3,1,2);
stem(n2,x2);
grid on;
xlabel('n2');
ylabel('Amplitude');
title('Second sequence');

n3=0:N-1;
subplot(3,1,3);
stem(n3,yn);
grid on;
xlabel('n3');
ylabel('Amplitude');
title('Convolved output');



exp 5

clc;
clear all;
close all;
x= input('Enter the sequence : ')
N=length(x)
xK=fft(x,N)
xn=ifft(xK)
n=0:N-1;
subplot (2,2,1);
stem(n,x);
xlabel('n ');
ylabel('amplitude');
title('input sequence');
subplot (2,2,2);
stem(n,abs(xK));
xlabel('n ');
ylabel('magnitude');
title('magnitude response');
subplot (2,2,3);
stem(n,angle(xK));
xlabel('n');
ylabel('phase');
title('Phase responce');
subplot (2,2,4);
stem(n,xn);
xlabel('n ');
ylabel('amplitude');
title('IFFT');