1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Fourier Series/Transformations and Convolution

  1. Mar 5, 2014 #1
    1. The problem statement, all variables and given/known data

    (f*g)(x) = integral from -pi to pi of (f(y)g(x-y))dy
    f(x) = ∑cneinx
    g(x) = ∑dneinx

    en is defined as the Fourier Coefficients for (f*g) {the convolution} an is denoted by:

    en = 1/(2pi) integral from -pi to pi of (f*g)e-inx dx

    Evaluate en in terms of cn and dn

    Hint: somewhere in the integral, the substitution z = x - y might be helpful.

    2. Relevant equations

    For convolution, if C(x) = the integral from -infinity to infinity of (f(y)g(x-y))dx, the Fourier transform of C(x) is equal to the Fourier transform of f times the Fourier transform of g.

    3. The attempt at a solution

    I'm really not too sure where to begin with this other than understanding the definition in the Relevant Equations section. Before this problem, all we were told was this definition. I do not see any way this is related to the Fourier series mentioned in the problem, let alone how to incorporate just the coefficients of the series into the integral.

    Any help to point me in the right direction would be greatly appreciated.
     
  2. jcsd
  3. Mar 5, 2014 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Do you understand how that result, the theorem you mention in the relevant equations section, was obtained? If not, start there. You might try something similar in solving the problem.
     
  4. Mar 6, 2014 #3
    I am pretty confused. The only thing jumping out to me on what to do is to substitute substitute (f*g)(x) = integral from -pi to pi of (f(y)g(x-y))dy into the integral for en and work it like a double integral. I am not exactly too sure if this would work though because I cannot think of where cn and dn would come in though (since he wants the answer in terms of those coefficients).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Fourier Series/Transformations and Convolution
Loading...