[R] fft: characteristic function to distribution

Prof Brian Ripley ripley at stats.ox.ac.uk
Wed Apr 30 16:38:41 CEST 2008

On Wed, 30 Apr 2008, Thomas Steiner wrote:

> The characteristic function is the inverse Fourier transform of the
> distribution function. The characteristic function of a normaly
> distributed random variable is exp(-t^2/2).

The fft is a discrete Fourier transforn, not a continuous one.
Further in each case where the normalizing constants are placed and the 
units of frequecy differ from source to source.

?fft has references to exactly what it computes: please consult them.

> x=seq(-2,2,length=100)
> fft(pnorm(x),inverse=T)/length(x)
> exp(-x^2/2)
> Why aren't the inverse fft and the mentioned function the same?
> Thanks for help,
> Thomas
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Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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