Simpliefied setup.
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Assume I am given some function f(t).
I know that it is constructed as $f(t) = \sum\_{k=1...M} C\_k exp(2 \pi~ i~ w\_k t ) + noise(t)$.
where $noise(t)$ is some random set of numbers depending on $t$ (white noise if you like).
I need to estimate $C\_k$ and $w\_k$. 


Solution: I will make Fourier Transform $\hat f(\lambda)$ and will pick up those $\lambda= w\_k$ such that $\hat f(\lambda) > threshold$.
How should I choose this threshold ? (The question is probably not 100% well-posed, but hope idea is clear).


True setup.
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Now assume that $t$ is discrete e.g. $t= l/N$, for some $N$ and $l=1...N$.


And the problem is that $w\_k$ are do not of the form $l/N$.


**Difficulty** So the functions $exp(2 \pi~ i~ w\_k t )$ are NOT orthogonal on the 
discrete set $t=l/N$.


So there are some problems with making Fourier transform approach.



Given f(t) = \sum_k C_k exp(2 pi i w_k t ) + noise. Need to estimate C_k and w_k .
Looks like could take a look at [Prony's method](http://en.wikipedia.org/wiki/Prony%27s_method).


