Proofs of Convolution Properties: Step-by-Step Guide

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The discussion focuses on the proofs of two convolution properties: associativity, f * (g * h) = (f * g) * h, and the distributive property, (cf) * g = c(f * g) = f * (cg). The user seeks step-by-step guidance or links to detailed proofs, expressing confusion over the notation used. Clarification is provided that '*' denotes convolution, while juxtaposition (ab) indicates multiplication. The conversation emphasizes the need for clear explanations of these fundamental concepts in convolution.
ky2168
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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.
 
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What does each letter represent? How is a * b different from ab?
 
Reply

By * I mean convolution.

I would think most people take

ab

as product while

a * b

to be convolution.
 
f and g are obviously functions and c a constant.
 

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