Discrete transforms with Gaussian periods of cyclotomic fields as basis for set functions

Vladimir M. Chernov

doi:10.1117/12.302489

10 March 1998 Discrete transforms with Gaussian periods of cyclotomic fields as basis for set functions

Vladimir M. Chernov

Proceedings Volume 3348, Optical Information Science and Technology (OIST97): Computer and Holographic Optics and Image Processing; (1998) https://doi.org/10.1117/12.302489
Event: Optical Information Science and Technology, 1997, Moscow, Russian Federation

Abstract

In the paper algebraic foundations of fast algorithms like Rader's for discrete orthogonal transforms are analyzed. It is shown that the connection between discrete Fourier transform of length p (p is a prime) and cyclic convolution of length (p - 1) is defined by cyclic structure of Galois group of some cyclotomic field. A class of discrete orthogonal transforms with fast algorithms like Rader- Vinograd is introduced.

Citation Download Citation

Vladimir M. Chernov "Discrete transforms with Gaussian periods of cyclotomic fields as basis for set functions", Proc. SPIE 3348, Optical Information Science and Technology (OIST97): Computer and Holographic Optics and Image Processing, (10 March 1998); https://doi.org/10.1117/12.302489

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