- #1
cassiew
- 6
- 0
Homework Statement
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]
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?