MATLAB Convolution: Finding the Convolution of Two Functions with Step Inputs

[Les talons]

Homework Statement

Use MATLAB to find the convolution between
a) $f(t) = u(t) -u(t -3)$ and $g(t) = u(t) -u(t -1)$

Homework Equations

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?

 

[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.