Proofs of Convolution Properties: Step-by-Step Guide

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Homework Help Overview

The discussion revolves around the proofs of convolution properties in the context of functions, specifically focusing on the associative property and the behavior of convolution with constants. The original poster expresses difficulty in understanding these proofs and seeks clarification.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster requests step-by-step proofs for specific convolution properties and expresses uncertainty about their understanding. Some participants question the notation used, specifically the distinction between convolution and product.

Discussion Status

The discussion is currently exploratory, with participants clarifying terminology and notation. There is no consensus yet on the proofs themselves, as the original poster is seeking guidance rather than receiving it.

Contextual Notes

Participants are discussing basic properties of convolution, and there is an emphasis on understanding the notation and definitions involved. The original poster's request for detailed proofs suggests a need for foundational clarity.

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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