利用本原单位根构造正交变换

doi:10.3969/j.issn.1001-2400.2013.05.025

Abstract

Abstract:

A new orthogonal transform based on the primitive unit root in the integral ring is proposed, which summarizes the orthogonal transform in the residue class rings of integers, finite fields and the complex field as well as the polynomial transform, including Discrete Fourier Transform, Hadamard Transform and Chrestenson Transform. The symmetric Transform of Multiple Real Values, Discrete W Transform and Discrete Sine-type Transform can be derived from it. The orthogonality of the Discrete Sine-type Transform has been proved. All transforms possess a fast algorithm based on related of to the DFT. This paper is very beneficial to grasping typical transforms systematically and constructing a new transform.

Key words: pimitive unit root, orthogonal transform, discrete Sine-type transform, fast algorithm

SUN Jichao;ZHOU Kai;SHU Da. Using primitive unit roots to construct orthogonal transforms[J].J4, 2013, 40(5): 157-162.

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Using primitive unit roots to construct orthogonal transforms

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