Convolving two signals

Question

Calculate the convolution of the following signals (your answer will be in the form of an equation):
h[n] = δ[n-1] + δ[n+1], x[n] = δ[n-a] + δ[n+b]

I'm lost as to what I do with h and x. Do I simply multiply them? h[n]*x[n]? I programmed convolution with several types of blurs and edge detectors, but I don't see how to translate that knowledge to this problem. Please help!

Answer 1

Convolution is an operation distinct from multiplication. If h[n] = delta[n-a] represents an impulse at n=a, then the convolution of h and any function f[n] is equal to conv(h,f) = f[n-a], and you should be able to determine the answer to your question through superposition, since convolution and addition are both linear operators.

Answer 2

The convolution of h and x (hx) will be something like hx = SUM h[n-q]*x[n], where the sum is performed over all possible q's depending on the size of h. If h and x are infinite then the sum goes from -INF to +INF.

Answer 3

In this case, (and more so if you are unsure about convolution), it is convenient to do the convolution graphically, to grap the basics and relate that to the analytical formula.