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. > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
- References:
- Discrete Fourier Transforms
- From: "W.W. Sampson" <w.sampson@umist.ac.uk>
- Discrete Fourier Transforms