Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    HallsofIvy

    User Avatar
    Staff Emeritus
    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:
    image.png

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

    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

    Mark44

    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

    Mark44

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Sinusoidal and exponential series
  1. Exponential integral (Replies: 6)

Loading...