DFTs/ IDFTs using matrix multiplication, circular convolution

PROGRAM 1:
OBJECT: To write a program to compute “Circular convolution” of two sequences x(n) and h(n).
x(n) = { 1, -1, -2, 3, -1 }  and   h(n) = { 1, 2, 3 }

Procedure: Here we have used two user defined functions:

This is circular convolution function

function [y] = circonv(x,h,N)
for k=1:N
    y(k)=0;
    for i=1:N
        j=k-i+1
        if(j<=0)
            j=N+j;
        end;
        y(k)=y(k)+x(i)*h(j);
    end;
end;

This is zero padding function

function [x,h] = zeropadding(x,h,N);
N1=length(x);
N2=length(h);
if(N==N1)
    h=[h zeros(1,(N-N2))];
else
x=[x zeros(1,(N-N1))];
end;

main program

x=[1 -1 -2 3 -1];
h=[1 2 3];
L=max(length(x), length(h));
[x,h]=zeropadding(x,h,L);
[y]=circonv(x,h,L);
n=0:1:(L-1);
stem(n,y);
grid on;
title('CIRCULAR CONVOLUTION');
xlabel('TIME INDEX');
ylabel('AMPLITUDE');

Fig. 1: circular convolution by function call.

PROGRAM 2:
OBJECT: To find “circular convolution” using “DFT” and “IDFT” methods (using fft and ifft commands). Sequences are as given below:
x(n) = { 3, 4 , -2 , 0 , 1 , -4 }  and   h(n) = { 1 , -3 , 0 , 4 }

SOURCE CODE:

x=[3 4 -2 0 1 -4];
h=[1 -3 0 4];
l_x=length(x);
l_h=length(h);
L=max(l_x,l_h);
[x,h]=zeropadding(x,h,L);    %This will called "zeropadding" function written in previous program.
X=fft(x);
H=fft(h);
y1=X.*H;
y=ifft(y1);
n=0:1:(L-1);
stem(n,y);
grid on;
title('CIRCULAR CONVOLUTION USING DFT AND IDFT');
xlabel('TIME INDEX');
ylabel('AMPLITUDE');

RESULT:
y =
    15    -1   -30    18    17   -15
OUTPUT GRAPH:

Fig. 1: circular convolution using DFT and IDFT methods.

Index of DSP Lab Manual.