# Signals Processing convolution graph

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Emir Dönmez il 20 Apr 2023
conv(x(t),&(t+t0) what is the eqaul of this equation and how can i plot this equation's graph?
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Ganapathi Subramanian il 25 Apr 2023
Hi Emir,
It is my understanding that you are working on convolution and want to know how to perform convolution on time shifted signal [x(t)*x(t+t0)] and plot the graph. Below is the code to perform convolution for time shifted signal.
% Time step to make it a continuous signal
step=0.01;
t=-10:step:10;
% Let the input be a unit step signal
% x(t)
x=t>=0;
subplot(3,1,1);
plot(t,x);
% Let t0 be the value of time shift
% x(t+t0)
% Let t0 be 5
t0=5;
% Time shifted signal => x(t+t0) = x1(t1)
t0=-t0;
if(t0>0)
t1=t(1):step:t(end)+t0;
x1=[zeros(1,t0/step) x];
mini=t(1);
maxi=t1(end);
else
t1=t(1)+t0:step:t(end);
x1=[x zeros(1,abs(t0)/step)];
mini=t1(1);
maxi=t(end);
end
subplot(3,1,2);
plot(t1,x1);
% Convolution of x(t) and x(t+t0)
y=conv(x,x1);
% ty is the variable scale that matches length(y) with the time of input signal
ty=mini:(maxi-mini)/(length(y)-1):maxi;
% Plot the convolution result
subplot(3,1,3);
plot(ty,y);
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