Proving associativity and scalar multiplication of convolution

[ky2168]

I know this is elementary but I'm having trouble with proofs of some of the convolution properties:

1. f * (g * h) = (f * g) * h
2. (cf) * g = c(f * g) = f * (cg)

Please show me the proofs step by step or lead me to a link where the detailed proofs are displayed.

Sorry for such elementary questions. I don't know why I'm not seeing it.

 

[EnumaElish]

What does each letter represent? How is a * b different from ab?

 

[ky2168]

Reply

By * I mean convolution.

I would think most people take

ab

as product while

a * b

to be convolution.

 

[ky2168]

f and g are obviously functions and c a constant.