# Convolution in MATLAB

1. Sep 28, 2015

### Les talons

1. The problem statement, all variables and given/known data
Use MATLAB to find the convolution between
a) $f(t) = u(t) -u(t -3)$ and $g(t) = u(t) -u(t -1)$

2. Relevant equations

3. The attempt at a solution
t = -10: 0.1: 10;
f = heavisde(t) -heaviside(t -3);
g = heaviside(t) -heaviside(t -1);
t = -20: 0.1: 20;
c = conv(f, g);
plot(t, c)

The graph of the convolution has values from 0 to 10. I don't get how the convolution can get to 10 if the functions being convolved only have maximum values of 1. I changed the line to
c = 0.1*conv(f, g);
and this produced the right output. Why do I need to multiply by the step size?

2. Sep 28, 2015

### RUber

Convolution is a sum over element-wise products. To turn this into the equivalent approximation for the integral, you have to multiply by the step size. Think about the rectangular area. Matlab applies the linear algebra definition of convolution.