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Re: fft: characteristic function to distribution

by Prof Brian Ripley :: Rate this Message:

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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> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

--
Brian D. Ripley, ripley@...
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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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

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