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Re: Fast Fourier Transforms

• To: mathgroup at smc.vnet.net
• Subject: [mg21662] Re: Fast Fourier Transforms
• From: jenningsj at mail.utexas.edu (Jim Jennings)
• Date: Fri, 21 Jan 2000 04:00:13 -0500 (EST)
• Organization: The University of Texas at Austin
• References: <85p7u3$6je@smc.vnet.net> <8618rn$l80@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

In article <85p7u3$6je at smc.vnet.net>, "Burton" <Ctheurer at ecs.umass.edu> writes:
>     I am doing some analysis of acoustic data obtained from a pickup located
> on a machine.  The data is in the form of ordered pairs i.e. Time and
> voltage.  As far as I know fft in Mathematica only operates on a list of
> single numbers.  I have imported the voltage data (since the time is simply
> incremental) and performed an fft on that successfully.  My problem lays in
> interpreting this data.  I don't understand how to scale the x-axis of the
> fft plot to represent frequency.
>     Any suggestions would be appreciated.

You need to read up on FFT's and spectral analysis.  A good place to start
is the Numerical Recipies book by Press and others, but If you really want
to understand what you are doing you will probably need to get beyond that
book to things like Bracewell's textbook on Fouier transforms and the more
recent Briggs & Henson book on discrete Fouier transforms.

For one thing, if I am guessing correctly that what you really want is to
estimate the power spectrum, it is not just the Fourier transform of the
data.  It is the modulus squared of the transform.  Estimating the power
spectrum from your data with a discrete transform may also require some
windowing.  The details required to get all this right and understanding
what it means will require some study of the books I mentioned plus
careful attention to which FFT definitions are used in Mathematica.  I
have not used any of the add-on Mathematica packages for spectral and time
series analysis, but these may help as well...

-- 
Jim Jennings                                
Research Associate              jenningsj at mail.utexas.edu
Bureau of Economic Geology      (512) 471-4364 (voice)
University of Texas at Austin   (512) 471-0140 (fax)