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MathGroup Archive 2003

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Re: Discrete Fourier Transform

  • To: mathgroup at smc.vnet.net
  • Subject: [mg43863] Re: Discrete Fourier Transform
  • From: Mariusz Jankowski<mjankowski at usm.maine.edu>
  • Date: Thu, 9 Oct 2003 01:54:38 -0400 (EDT)
  • Organization: University of Maine System testbed server
  • References: <bm0juq$prl$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Catherine,

Fourier[x] gives you N=Length[x] Fourier coefficients. The resoution is 1/N Hz or 2 Pi/N radians per second (assuming, of course, that the samples of the time series x are spaced 1 second apart). To change the resolution pad the sequence with zeros:

Fourier[PadRight[x, M]]

For more details consult any modern undergraduate EE textbook on signals and systems, such as Oppenheim, or Haykin, or Carlson.

Mariusz  



>>Hello everyone,
>>
>>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.
>>
>>Do you know of any way to get around the problem?
>>
>>Thanks so much.
>>
>>Catherine Neish




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