MATLAB program to perform linear convolution using circular convolution

Program code

%linear convolution using circular convolution

clc;

clear all;

close all;

x=input('Please enter the first sequence x[n] = ');

h=input('Please enter the second sequence h[n] = ');

len_x=length(x);

len_h=length(h);

h=[h zeros(1,len_x-1)];

x=[x zeros(1,len_h-1)];

L=len_x+len_h-1;

for i=0:L-1

    for j=1:L-i;

        a(j+i,i+1)=x(j);

    end

end

for m=1:L-1

    for n=m+1:L

        a(m,n)=x(L-n+m+1);

    end

end

b=transpose(h);

y=a*b;

y=transpose(y);

subplot(311);

stem(x);

disp('The sequence obtained after linear convolution of x[n] with h[n], is given below. ');

disp(y);

grid on;

title('First sequence x[n] ');

subplot(312);

stem(h);

grid on;

title('Second sequence h[n] ');

subplot(313);

stem(y);

Example of output

Please enter the first sequence x[n] = [1 2 3 4 5 6]

Please enter the second sequence h[n] = [1 2 3 4 5 6]

The sequence obtained after linear convolution of x[n] with h[n], is given below.

     1     4    10    20    35    56    70    76    73    60    36

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MATLAB program to perform circular convolution of two signals

Program Code

%circular convolution

clc;

close all;

clear all;

x=input('Please enter the first sequence x[n] = ');

h=input('Please enter the second sequence h[n] = ');

L1=length(x);

L2=length(h);

Len=max(L1,L2);

x=[x zeros(1,Len-L1)];

h=[h zeros(1,Len-L2)];

for i=0:(Len-1)

    y(i+1)=0;

    for j=0:(Len-1)

        m=mod(i-j,Len);

        y(i+1)=y(i+1)+(x(j+1)*h(m+1));

    end

end

disp('Convoluted sequence of x[n] and h[n] is given below: ');

disp(y);

subplot(311);

stem(x);

title('First sequence x[n]');

grid on;

subplot(312);

stem(h);

title('Second sequence h[n]');

grid on;

subplot(313);

stem(y);

title('Convoluted sequence ');

grid on;

Example of Output

Please enter the first sequence x[n] = [1 3 2 1]
Please enter the second sequence h[n] = [2 1 2]
Convoluted sequence of x[n] and h[n] is given below: 
     7     9     9    10

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MATLAB program to perform linear convolution of two signals ( without using MATLAB function)

Program Code

clc;

close all;

clear all;

xt=input('Please enter the input sequence in time domain x[n]= ');

lxt=length(xt);

ht=input('Please enter the impulse sequence h[n]= ');

lht=length(ht);

ext=[xt zeros(1,(lht-1))];

eht=[ht zeros(1,(lxt-1))];

xdft=fft(ext);

hdft=fft(eht);

freqm=xdft.*hdft;

yt=[ifft(freqm)];

display('The convoluted sequence is given below');

disp(yt);

subplot(311);

stem(xt);

xlabel('Time');

ylabel('Magnitude');

title('Input sequence x[n]');

subplot(312);

stem(xt);

xlabel('Time');

ylabel('Magnitude');

title('Input sequence 1');

subplot(313);

stem(yt);

xlabel('Time');

ylabel('Magnitude');

title('Convoluted sequence');

Example of Output

Please enter the input sequence in time domain x[n]= [1 2 3 4 5 6]

Please enter the impulse sequence h[n]= [1 2 3 4 5 6]

The convoluted sequence is given below

  Columns 1 through 5 

    1.0000    4.0000   10.0000   20.0000   35.0000

  Columns 6 through 10 

   56.0000   70.0000   76.0000   73.0000   60.0000

  Column 11 

   36.0000

Matlab program to find the linear convolution of two signals (using matlab functions)

Program Code

%linear convolution (using matlab functions)
clc;
close all;
clear all;
x1=input('Please enter the input sequence x[n]= ');
x2=input('Please enter the starting time index of x[n]= ');
h1=input('Please enter the impulse response h[n]= ');
h2=input('Please enter the starting time index of h[n]= ');
y=conv(x1,h1);
n=x2+h2:length(y)+x2+h2-1;
display('The convoluted sequence is given below:');
y
stem(n,y);
xlabel('Time');
ylabel('Amplitude');
title('Linear Convolution');

Example of Output

Please enter the input sequence x[n]= [4 3 1 2]
Please enter the starting time index of x[n]= -2
Please enter the impulse response h[n]= [1 4 3]
Please enter the starting time index of h[n]= -1
The convoluted sequence is given below:

y =


     4    19    25    15    11     6

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