I'm currently working through some convolution examples and I'm unsure of something.
The question is given as:
Consider the input \$\ x(n) = u(n) \$ and the impulse response \$\ h(n) = (0.5)^n u(n) \$ for a certain system. What is the output of the system?
From the convolution equation, I understand that the first step produces: \$\ y(n) = \sum\limits_{m=-\infty}^\infty u(m)(.5)^{n-m} u(n-m) \$
The question goes on to say:
But since \$\ u(m) = 1 \$ for \$\ n \ge 0 \$ and both \$\ x(n) \$ and \$\ h(n) \$ start at \$\ n = 0 \$, we have \$\ y(n) = \sum\limits_{m=0}^{m=n} = (.5)^{n-m} \$
I understand that \$\ u(m) \$ disappears as it is a constant, but how is \$\ u(n-m) \$ removed?
Thanks in advance for any help on this.
EDIT: Additionally, why do the limits change from +/- infinity to \$\ m=n \$ and \$\ n = 0 \$?