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MathGroup Archive 2003

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Re: Discrete Fourier Transform

  • To: mathgroup at smc.vnet.net
  • Subject: [mg43871] Re: Discrete Fourier Transform
  • From: Bill Rowe <readnewscix at mail.earthlink.net>
  • Date: Thu, 9 Oct 2003 01:55:10 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On 10/8/03 at 4:47 AM, cdneish at interchange.ubc.ca (Katie Neish) wrote:

> I am attempting to perform a discrete Fourier transform on a time series
> using Mathematica 4.0.  (I'd like to determine the period of the signal.)
> Unfortunately, I noticed that I cannot control the frequency resolution of
> this transform.  I also have no idea what units the frequency is in.

The frequency resolution of the transform is controlled by the size of the sampling interval in the original data and the number of data samples. Basically, you cannot detect frequencies above 2/T or below 1/(n T) where T is the sampling interval and n is the number of data samples. Also, the frequency units are determined by the size of the sampling unit.

If you are going to use Mathematica to do Fourier analysis of data, it would be a very good idea to find a couple of good text on the subject. You should be able to find sufficient information if you look for text on either Fourier transforms or signal processing. You also might find something useful in advanced texts on statistical methods. But I would recommend more basic texts on Fourier transforms or signal processing since the discussions I've seen in advanced statistics texts usually assume a pretty good understanding of Fourier methods.
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