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Fourier Coefficients

  1. Jun 3, 2008 #1
    Hi,

    I was wondering if it is possible to express the norm of a function in terms of fourier coefficient. If so, how do you go through it if given a particular function.

    Thanks
     
  2. jcsd
  3. Jun 3, 2008 #2
    What norm? The [tex]L^2[/tex]-norm can be expressed, and it is the square root of the sum of the squares of the coefficients.
     
  4. Jun 5, 2008 #3
    Here is a sample question:

    What are the fourier coefficients of the function f(x)=ae^(-ix)+b+ce^(ix)? And express the norm in terms of fourier coefficients.

    They don't mention if it is the L^2 norm or not.
     
  5. Jun 6, 2008 #4

    rbj

    User Avatar

    well, it's only the L2 norm (a measure of energy) in which the L2 norm of the time-domain function (over one period) is equal to the L2 of the frequency-domain data (the Fourier coefficients).

    i think the L2 norm of your f(x) is a2 + b2 + c2.
     
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