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MathGroup Archive 1999

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Re: Discrete Fourier Transforms

  • To: mathgroup at smc.vnet.net
  • Subject: [mg18093] Re: [mg18075] Discrete Fourier Transforms
  • From: Ken Levasseur <Kenneth_Levasseur at uml.edu>
  • Date: Thu, 17 Jun 1999 12:26:34 -0400
  • Organization: UMass Lowell Mathematical Sciences
  • References: <199906150543.BAA13321@smc.vnet.net.>
  • Sender: owner-wri-mathgroup at wolfram.com

Bill:

If you list the positive powers of any nth root of unity: w, w^2, ...
w^(n-1), their reciprocals (powers of w^(-1)) will be the reversal of
that list: w^(n-1), ..., w^2, w.  The same is true in a finite field. 
This is why the output values for the EE Fourier Transform would be
reversed.  The output list is not a list of reciprocals however, just a reversal.

Ken Levasseur
UMass Lowell

"W.W. Sampson" wrote:
> 
> In the Mathematica Book for version 3, it states in Section 3.8.3,  with
> reference to Fourier Transforms, "In electrical engineering, the sign of
> the
> exponent is typically reversed, leading to a list of values which is
> reversed."
> 
> As the output from the Fourier Transformis symmetrical, should this be
> that the values are the reciprocal?
> 
> Bill
> 
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> Dr W.W. Sampson, Department of Paper Science, UMIST,
> Manchester, M60 1QD, UK. Email: w.sampson at umist.ac.uk
> Phone:+44-(0)161-200-3898    Fax:+44-(0)161-200-3858.
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


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