Fourier series inverse problem

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given the fourier series



$$ f(x) = fraca_02+ sum_n=1^inftya(n)cos(nkx)+sum_n=1^inftyb(n)sin(nkx) $$



'k' is a real number positive



then here is the 'inverse problem'



imagine i know the values of $ a(n)= g(n)$



where $ g(n) $ is the inverse of a polynomial or a trigonommetric function



then how could i recover the function from the coefficients?







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  • 1




    The function is already given by the coefficients using the above equality. Do you intend to reconstruct a nice formula for the function from its Fourier coefficients, when it has one?
    – Ian
    Aug 9 at 18:22















up vote
0
down vote

favorite












given the fourier series



$$ f(x) = fraca_02+ sum_n=1^inftya(n)cos(nkx)+sum_n=1^inftyb(n)sin(nkx) $$



'k' is a real number positive



then here is the 'inverse problem'



imagine i know the values of $ a(n)= g(n)$



where $ g(n) $ is the inverse of a polynomial or a trigonommetric function



then how could i recover the function from the coefficients?







share|cite|improve this question
















  • 1




    The function is already given by the coefficients using the above equality. Do you intend to reconstruct a nice formula for the function from its Fourier coefficients, when it has one?
    – Ian
    Aug 9 at 18:22













up vote
0
down vote

favorite









up vote
0
down vote

favorite











given the fourier series



$$ f(x) = fraca_02+ sum_n=1^inftya(n)cos(nkx)+sum_n=1^inftyb(n)sin(nkx) $$



'k' is a real number positive



then here is the 'inverse problem'



imagine i know the values of $ a(n)= g(n)$



where $ g(n) $ is the inverse of a polynomial or a trigonommetric function



then how could i recover the function from the coefficients?







share|cite|improve this question












given the fourier series



$$ f(x) = fraca_02+ sum_n=1^inftya(n)cos(nkx)+sum_n=1^inftyb(n)sin(nkx) $$



'k' is a real number positive



then here is the 'inverse problem'



imagine i know the values of $ a(n)= g(n)$



where $ g(n) $ is the inverse of a polynomial or a trigonommetric function



then how could i recover the function from the coefficients?









share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Aug 9 at 18:20









Jose Garcia

4,01511235




4,01511235







  • 1




    The function is already given by the coefficients using the above equality. Do you intend to reconstruct a nice formula for the function from its Fourier coefficients, when it has one?
    – Ian
    Aug 9 at 18:22













  • 1




    The function is already given by the coefficients using the above equality. Do you intend to reconstruct a nice formula for the function from its Fourier coefficients, when it has one?
    – Ian
    Aug 9 at 18:22








1




1




The function is already given by the coefficients using the above equality. Do you intend to reconstruct a nice formula for the function from its Fourier coefficients, when it has one?
– Ian
Aug 9 at 18:22





The function is already given by the coefficients using the above equality. Do you intend to reconstruct a nice formula for the function from its Fourier coefficients, when it has one?
– Ian
Aug 9 at 18:22
















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