[R] fft: from characteristic funtion to density function

Matthias Kohl Matthias.Kohl at stamats.de
Thu Sep 11 19:46:39 CEST 2008

take a look at


Jindan Zhou wrote:
> Hello all!
> I've posted the question before but I am still struggling for an
> answer, please help if you can;-)
> Suppose a discrete series of data is generated by the following
> equation:
> CF=exp(-(t^2)/2)
> which is the characteristic function of a random variable X with
> standard normal distribution, how do I *numerically* solve for its
> probability density function? i.e., obtain a series of data that plots
> a well know bell-shape curve? Or, find x such that Pr(X<x)=0.05?
> I have no problem to derive the forward and inverse Fourier equation
> pair, but just no clue on numerical method. A working code on this
> simplest exercise
> would clear off many, many of my confusions
> I have generated CF with t of 256 points equally spaced between -4 to
> 4 in Excel, but don't know
> how to proceed.
> Thanks for your help!
> Jindan
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Dr. Matthias Kohl

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