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?
fourier-analysis
add a comment |Â
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?
fourier-analysis
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?
â Ian
Aug 9 at 18:22
add a comment |Â
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?
fourier-analysis
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?
fourier-analysis
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?
â Ian
Aug 9 at 18:22
add a comment |Â
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?
â 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?
â 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?
â Ian
Aug 9 at 18:22
add a comment |Â
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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?
â Ian
Aug 9 at 18:22