Fourier transforms from a generalised trace map

Horadam, K and Rao, A 2006, 'Fourier transforms from a generalised trace map', in Proceedings of the 2006 IEEE International Symposium on Information Theory, Seattle, Washington, USA, 9-14 July 2006, pp. 1080-1084.


Document type: Conference Paper
Collection: Conference Papers

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Title Fourier transforms from a generalised trace map
Author(s) Horadam, K
Rao, A
Year 2006
Conference name 2006 IEEE International Symposium on Information Theory
Conference location Seattle, Washington, USA
Conference dates 9-14 July 2006
Proceedings title Proceedings of the 2006 IEEE International Symposium on Information Theory
Publisher IEEE
Place of publication NJ, USA
Start page 1080
End page 1084
Total pages 5
Abstract The class of Generalised Hadamard Transforms includes the Fourier, Generalised, Discrete Fourier, Walsh-Hadamard, Complex Hadamard and Reverse Jacket Transforms. The Generalised Hadamard Transforms may by partly classified by signal length, by group of entries in the transform matrix and by a recently introduced third parameter, the jacket width of the transform matrix. Here we introduce a weighted trace map, which realises the Fourier Transform as an exponential weighted sum of Galois Ring traces. We give examples of Fourier Transforms with jacket width 0, jacket width 1 and maximum jacket width (half the signal length). We show the Fourier Transforms of length 4k with entries in {±1, ±i} obtained using the weighted trace map from the Galois Ring GR(4,k) have jacket width 2k-1
Subjects Coding and Information Theory
Keyword(s) Fourier transforms
trace map
DOI - identifier 10.1109/ISIT.2006.261950
Copyright notice © 2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
ISBN 1424405041
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