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Re: fourier transform of interpolating function

• To: mathgroup at smc.vnet.net
• Subject: [mg55155] Re: fourier transform of interpolating function
• From: Jon Harrop <usenet at jdh30.plus.com>
• Date: Tue, 15 Mar 2005 00:21:37 -0500 (EST)
• Organization: Flying Frog Consultancy Ltd.
• References: <d0rofq$2cp$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

dumb_founded wrote:
> I am trying to get the Fourier tranform of an interpolating function,
> but the function Fourier[] only accepts a data table.  What can I do?
> I am sure some option is available that someone can inform me of.

It sounds like you've got some reading to do. :-)

Basically, your question probably isn't well defined. It could be taken to
mean that you want the analytic Fourier transform of a piecewise function
of splines, but I think this is probably not what you want.

You probably want to compute the FFT of a discrete sampling of your
interpolation function. Peter Pein suggested using Table to extract a
discrete sampling and then applying Fourier to get the DFT. This is a start
but the "x" values of your interpolation function are then being discarded
so the result needs to be multiplied by a phase factor and scaled in "x" to
represent the correct (Nyquist) frequency range and scaled in "y" to
represent amplitude (i.e. without a factor of "n").

-- 
Dr Jon D Harrop, Flying Frog Consultancy
http://www.ffconsultancy.com