(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let f,g be two continuous, periodic functions bounded by

[tex]

[-\pi,\pi]

[/tex]

Define the convolution of f and g by

[tex]

(f*g)(u)=(\frac{-1}{2\pi})\int_{-\pi}^{\pi}f(t)g(t-u)dt.

[/tex]

Show that

[tex]

(f*g)(u)=(g*f)(u)

[/tex]

3. The attempt at a solution

I think the way I'm supposed to do this is by interchanging variables, but I'm stuck. If I let k=t-u and try to switch the variables around, I end up with (-1/2pi) times the integral of g(k)f(k+u)dk. Am I doing this wrong? Is there a better way to solve this?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Prove Convolution is Commutative

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