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I am looking for a nice way to calculate the FT of the following function

$f(x)=\biggl(\sum_{n=1}^{c}~a_n~e^{-\frac{i}{2}~x~b_n}\biggr)^d$,

where $d,c>0$, $a_n$ and $b_n$ are real coefficients, strictly monotonously rising in $n$ and $x$ is the free variable and $c$ might go to $\infty$.

I used mathematica to calculate it, but without specification of $d$ and when $c\to\infty$, there is no way that the programme will do it.

Any helpful ideas? Thanks!!

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    the domain of x should be going from 0 till infinity.2012-08-05

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If $d$ is a positive integer, then you can use the multinomial theorem to expand your expression then take the Fourier transform with the appropriate condition on $\sum b_k $.

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    @Hamurabi:It has uses in electrical engineering. Read [here](http://en.wikipedia.org/wiki/Dirac_comb)2012-08-05