4. To perform linear convolution from circular convolution and vice versa

 Code:

clc;

clear all;

close;

//input sequences

x=[1,2,0,3,4,1];

h=[2,0,1,3,1];

//find length of input sequences

nx=length(x);

nh=length(h);

N=nx+nh-1; // Length of linear convolution

M=max(nx,nh); // Length of circular convolution

Y1=conv(x,h);//Linear convolution

//Circular convolution

x_len=[x,zeros(1,M-nx)];

h_len=[h,zeros(1,M-nh)];

DFT_x=fft(x_len);

DFT_h=fft(h_len);

DFT_xh=DFT_x.*DFT_h;

circ_xh=ifft(DFT_xh);

//Circular Convolution from linear convolution

for i=1:M

if (i<=(N-M)) then

Y2 (i)=Y1(i)+Y1(i+M);

else

Y2(i)=Y1(i);

end

end

//linear cnvolution from circular convolution

X=[x,zeros(1,nh-1)];

H=[h,zeros(1,nx-1)];

x_dft=fft(X);

h_dft=fft(H);

xh_dft=x_dft.*h_dft;

Y3= ifft(xh_dft);

//Display various sequences on console window

disp(x,"Input Sequence x");

disp(h,"Input Sequence h");

disp(Y1,"Linearly Convolved sequence using conv function");

disp(circ_xh,"Circularly Convolved sequence using fft

function");

disp(Y3," Linear Convolution from Circular Convolution")

disp(Y2',"Circular Convolution from Linear Convolution")

//Plot various sequences

subplot(2,2,1);

xlabel("Time");

ylabel("Amplitude");

title("Input Sequence x(n)")

a=gca();

a.x_location="origin";

a.y_location="origin";

plot2d3(x);

subplot(2,2,2);

xlabel("Time");

ylabel("Amplitude");

title("Input Sequence h(n)")

a=gca();

a.x_location="origin";

a.y_location="origin";

plot2d3(h);

subplot(2,2,3);

xlabel("Time");

ylabel("Amplitude");

title("Circular Convolution from Linear Convolution")

a=gca();

a.x_location="origin";

a.y_location="origin";

plot2d3(Y2);

subplot(2,2,4);

xlabel("Time");

ylabel("Amplitude");

title("Linear Convolution from Circular Convolution")

a=gca();

a.x_location="origin";

a.y_location="origin";

plot2d3(Y3);