[R] fft: from characteristic funtion to density function

[Jindan Zhou]

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