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Fourier Coefficients 
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#1
Jun308, 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 


#2
Jun308, 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.



#3
Jun508, 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. 


#4
Jun608, 12:26 AM

P: 2,251

Fourier Coefficients
well, it's only the L^{2} norm (a measure of energy) in which the L^{2} norm of the timedomain function (over one period) is equal to the L^{2} of the frequencydomain data (the Fourier coefficients).
i think the L^{2} norm of your f(x) is a^{2} + b^{2} + c^{2}. 


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