The eigenstructure of finite field trigonometric transforms

被引：14
|
作者：
Lima, J. B. [1 ]
Campello de Souza, R. M. [2 ]
Panario, D. [3 ]
机构：
[1] Univ Pernambuco, Polytech Sch Pernambuco, BR-50750470 Recife, PE, Brazil
[2] Univ Fed Pernambuco, Dept Elect & Syst, BR-50740530 Recife, PE, Brazil
[3] Carleton Univ, Sch Math & Stat, Ottawa, ON K1S 5B6, Canada
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2011年 / 435卷 / 08期
关键词：
Eigenvalues; Eigenvectors; Finite fields; Trigonometric transforms; COSINE; SINE;
D O I：
10.1016/j.laa.2011.03.031
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we discuss the eigenstructure of finite field trigonometric transforms (FFTT). This transform family includes different types of cosine and sine transforms that correspond, in the finite field case, to the well known discrete cosine and sine transforms defined over the real numbers. More specifically, we determine the eigenvalues of the FFTT matrices and study their multiplicities. We propose procedures for constructing the associated eigenvectors. Applications of the developed theory to multiuser communication systems and error-correcting codes are also suggested. (C) 2011 Elsevier Inc. All rights reserved.
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页码：1956 / 1971
页数：16
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