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Sinusoidal and exponential series

  1. May 2, 2014 #1
    If is possible to expess periodic functions as a serie of sinusoids, so is possible to express periodic functions with exponential variation through of a serie of sinusoids multiplied by a serie of exponentials? Also, somebody already thought in the ideia of express any function how a serie of exponential?
  2. jcsd
  3. May 2, 2014 #2


    User Avatar
    Science Advisor

    What do you mean by "periodic functions wit exponential variation"?
  4. May 2, 2014 #3
    An exemple of a periodic function that can be approximate by fourier series is:

    And another exemple of a "periodic function with exponential variation" is a function like this:

    So, if exist a exponential factor in the fourier series, this serie would be perfect for represent this second graph. Yeah!?
  5. May 2, 2014 #4


    Staff: Mentor

    The function in the graph is not periodic. For a periodic function whose period is p, f(x) = f(x + p), for any x.
  6. May 2, 2014 #5
    True! But, what say about a fourier serie with factor exponential?
  7. May 2, 2014 #6


    Staff: Mentor

    The Fourier series for a function is periodic, but if you multiply that series by an exponential function, the product is no longer periodic. I'm not sure I understand what you're asking, though.
  8. May 2, 2014 #7
    The fourier series, roughly speaking, is ##f(t) = \sum_{-\infty }^{+\infty } A_\omega \cos(\omega t - \varphi_\omega ) \Delta \omega ##, I was thinking in a serie like this: ##f(t) = \sum_{-\infty }^{+\infty } \sum_{-\infty }^{+\infty } A_{\omega \sigma} \exp(\sigma t) \cos(\omega t - \varphi_{\omega \sigma}) \Delta \omega \Delta \sigma## with the intention of express any function through this serie.
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