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

Fourier transform vs Inner product

  1. Mar 13, 2014 #1
    So the complex exponential Fourier series form an orthonormal basis for the space of functions. A periodic function can be represented with countably many elements from the basis, and an aperiodic function requires uncountably many elements.

    Given a signal, we can find the coefficients of the exponentials in two ways:
    1) Fourier transform
    2) Inner product with that complex exponential

    Though these two formulas are similar, they are not identical. So how could they both possibly give us the coefficient of a complex exponential?

    Thanks!

    BiP
     
  2. jcsd
  3. Mar 13, 2014 #2

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Can you please show the formulas you are comparing? There are several different conventions in use. Also, please clarify whether you are talking about Fourier series or Fourier transforms. You mentioned both.
     
  4. Mar 13, 2014 #3

    mathman

    User Avatar
    Science Advisor
    Gold Member

    [quotr]A periodic function can be represented with countably many elements from the basis, and an aperiodic function requires uncountably many elements.
    [/quote]
    What do have in mind? The basis has only a countable number of elements. Are you mixing Fourier series and Fourier transdforms?
     
  5. Mar 13, 2014 #4

    AlephZero

    User Avatar
    Science Advisor
    Homework Helper

    But not necessarily uncountably many non-zero elements. For example ##\cos t + \cos \pi t##.

    But I agree with the other posters, it's hard to figure out exactly what your OP is asking.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Fourier transform vs Inner product
  1. Inner product (Replies: 3)

  2. Inner product (Replies: 2)

  3. Inner product (Replies: 2)

  4. Inner Product (Replies: 10)

  5. Inner Products? (Replies: 7)

Loading...