How should I fix my convolutional integral

Hello all,

Actually, I am trying to convolve two functions (f and y)using the following MATLAB code:

close all;
clear all;
clc;
%set time vector
t0=0;
tf=100;
N=10000;
dt=(tf-t0)/N;
t=t0:dt:tf;
T0=60;
alpha=1;
beta=0.01;

%construct the firxt part of the convolution
for i=1:length(t)
  if(t(i)<=T0)   
    y(i)=0;
  else 
    y(i)=alpha+beta*(t(i)-T0);
  end
end
%plot y(t)
subplot(1,2,1);
plot(t,y,'LineWidth',2);
title('y(t)');

%Second function of the convolution
f2= 0.08787*exp(-((t-63.08)/1.593).^2);

%Convolution of these 2 functions
z=conv(y,f2,'full');
con = z*dt;
subplot(1,2,2);
plot(t,f2,'LineWidth',2);
title('f2');
t = (1:length(con))*dt ;
hold on;
plot(t,con,'LineWidth',2);

I tried to use the guidlines in the following link to run a full convolutional integral :

https://www.mathworks.com/matlabcentral/answers/379866-regarding-calculating-convolution-in-matlab

Here are my results:

This result seems not to be reasonable because both my functions start rising at x=60 but my convolution starts rising at x=120. Can someone helps me with this problem.

[Matt J]

This result seems not to be reasonable because both my functions start rising at x=60

There's nothing unreasonable about that. That is theoretically what should happen if both functions start at t=60. For the convolution result to start at t=60, you need one of the signals to start at t=0.

Answer 1

[Matt J]

This might be what you want,

subplot(1,2,1);
ty=t;
plot(ty,y,'LineWidth',2);
title('y(t)');

%Second function of the convolution
f2= 0.08787*exp(-((t-63.08)/1.593).^2);

%Convolution of these 2 functions


z=conv(y,f2(find(f2,1):end),'same');
con = z*dt;
subplot(1,2,2);
  plot(ty,f2,'LineWidth',2);
  title('f2');

  hold on;
  tc=linspace(0,1,numel(con));
  tc=tc/tc(2)*dt;
  plot(tc,con,'LineWidth',2);
  hold off

[Faezeh Manesh]

Hello Matt,

Thanks alot for your quick reply. Actually, I think the result of the convolution should be similar to what you obtained and I am interested in such results. But I was wondering what is the correct answer of the convolutional integral? Is the one that you obtained could be assumed as the correct result? Because you ignored the initial zero parts of the second function

[Matt J]

As I said in my comment above,

https://www.mathworks.com/matlabcentral/answers/509971-how-should-i-fix-my-convolutional-integral#comment_807733

I think you've had the correct result from the very beginning.

[Steve Chou]

This chart is more clear to read.