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

Signal and system

  1. Aug 7, 2010 #1

    Rsw

    User Avatar

    what is the difference between Fourier series and Fourier transforms ?
     
  2. jcsd
  3. Aug 7, 2010 #2
    Fourier series is an approximation of periodic functions, but Fourier transform is applied to the functions which isn't periodic(period = infinite).
     
    Last edited: Aug 7, 2010
  4. Aug 7, 2010 #3
    Fourier transform(FT) is the generalization of Fourier series. In FT you get frequency spectrum of a function f (if FT exists for f) and instead of spectrum you get discrete frequencies if f is periodic.

    Note: Both FT and fourier series are approximations of f
     
  5. Aug 7, 2010 #4
  6. Aug 7, 2010 #5
    I'd like to clarify that FT and FS are not approximations. Both are mathematical transforms that allow perfect reconstruction of the original function. For example, what is the Fourier Series of cos(x)? Hmmm, seems exact to me.

    Where the approximations come in is when you have an infinite series or a transform that extends to infinity. Then, you may decide to truncate the series or band-limit the transform, when using them to reconstruct the original function. Even if they are not infinite, you could still truncate/band-limit. Hence, you could say that a truncated FS or a band limited FT are approximations.
     
  7. Aug 8, 2010 #6

    Rsw

    User Avatar

    thanks 4 give me such replies........
     
  8. Aug 8, 2010 #7

    Rsw

    User Avatar

    can u tell me about some good books for "digital electronics"???????
    where i can clear my concept of "encoder,decoder and sequential circuits" and verilog of it also.
     
  9. Aug 8, 2010 #8
    Last edited by a moderator: Apr 25, 2017
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Signal and system
  1. Signal & Systems (Replies: 6)

  2. Signal & system (Replies: 5)

  3. Signals and Systems. (Replies: 4)

Loading...