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Re: Library for FT alpha-Stable ch.f. (fwd)
At Wed, 2 Jul 2008 11:55:32 -0600 (MDT),
James Theiler wrote:
> I reading thru the source code for the Levy library written for GNU. The statistical model that we are studying is like alpha-stable as only the ch.f. is in closed form. It will be presented this autumn in Melbourne, AU.
>
> Have you already considered using Fast Fourier transform for the Fourier transform integral?
> p(x) dx = (1/(2 pi)) \int dt exp(- it x - |c t|^alpha)
> If so, was the Frequency Sampling Technique applied in FFT/IFFT adaptive to the alpha parameter for faster computation? Or was there a bound placed on alpha to imply out Nyquist frequency for your IFFT/FFT? I look forward to your input. Thank you for your time and consideration.
The FFT method was too complicated for our needs as a general purpose
library so I did not look at it. We only provide cumulative
distribution functions when they are available in closed form.
--
Brian Gough