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Fourier Coefficients

by sristi89
Tags: coefficients, fourier
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sristi89
#1
Jun3-08, 08:49 PM
P: 8
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
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jostpuur
#2
Jun3-08, 09:52 PM
P: 2,023
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.
sristi89
#3
Jun5-08, 09:36 AM
P: 8
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.

rbj
#4
Jun6-08, 12:26 AM
P: 2,251
Fourier Coefficients

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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