Deconvolution help

[davedude82]

I don't even know where to start with this problem. I need to deconvolute a function g(B) in order to determine the prefactors $a_n$.

Here's what I have:
h(f,B) is a Gaussian function
g(B) is the unknown function
i(B) is an inhomogeneous function and a convolution of g(B) and h(f,B)

i(B)=g(B)*h(f,B)=$\int_{n=-\infty}^\infty dB g(B) h(f,B))$

I was given the following suggestion for g(B) either to use a Taylor expansion or a Fourier series:
g(B)=$\sum_{n=0}^\infty a_n sin(n B)$ if choosing Fourier.

I was told that if I do it right, I will end up getting an expression for a_n such that:
$a_n$=$\frac{\int i(B)dB}{\int h(f,B)dB}$
I need to find the expression for a_n. I don't even know where to start looking. I hope this makes sense and someone can help me.

 

[Deleted member 4993]

I need to deconvolute a function g(B) in order to determine its prefactors a_n. Here's what I have:
h(f,B) is a Gaussian function
g(B) is the unknown function

i(B) is an inhomogeneous function and a convolution of g(B) and h(f,B)
i(B)=g(B)⊗h(f,B)=\int_{n=-\infty}^\infty dB g(B) h(f,B))

I was given the following suggestion for g(B) either to use a Taylor expansion or a Fourier series:
g(B)=\sum_{n=0}^\infty a_n sin(n B)

I need to find the expression for a_n, but I'm having trouble figuring it all out.

Duplicate Post:

http://mathoverflow.net/questions/211051/how-to-deconvolute-an-integrated-function

 

[stapel]

Also posted here.

 

[Ishuda]

I don't even know where to start with this problem. I need to deconvolute a function g(B) in order to determine the prefactors $a_n$.

Here's what I have:
h(f,B) is a Gaussian function
g(B) is the unknown function
i(B) is an inhomogeneous function and a convolution of g(B) and h(f,B)

i(B)=g(B)*h(f,B)=$\int_{n=-\infty}^\infty dB g(B) h(f,B))$

I was given the following suggestion for g(B) either to use a Taylor expansion or a Fourier series:
g(B)=$\sum_{n=0}^\infty a_n sin(n B)$ if choosing Fourier.

I was told that if I do it right, I will end up getting an expression for a_n such that:
$a_n$=$\frac{\int i(B)dB}{\int h(f,B)dB}$
I need to find the expression for a_n. I don't even know where to start looking. I hope this makes sense and someone can help me.

Do you know what a convolution is? If so, why are you not using standard notation [and, since it is non-standard, just exactly what do you mean by the integrals? You integrate over B yet still have a function of B and the dependence of g on f has disappeared somewhere]. If not, you need to know what that is before you work the problem since the problem involves a convolution.