Signals Processing convolution graph

conv(x(t),&(t+t0) what is the eqaul of this equation and how can i plot this equation's graph?

Answer 1

[Ganapathi Subramanian]

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);