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
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.
"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
> exponent is typically reversed, leading to a list of values which is
> As the output from the Fourier Transformis symmetrical, should this be
> that the values are the reciprocal?
> 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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