Fractional Fourier, Hartley, Cosine and Sine Number-Theoretic Transforms Based on Matrix Functions

作     者：Lima, Paulo Hugo E. S. Lima, Juliano B. Campello de Souza, Ricardo M. 

作者机构：Univ Fed Pernambuco Dept Elect & Syst Recife PE Brazil 

出 版 物：《CIRCUITS SYSTEMS AND SIGNAL PROCESSING》 (电路、系统和信号处理)

年 卷 期：2017年第36卷第7期

页      面：2893-2916页

核心收录：

学科分类：0808[工学-电气工程] 0809[工学-电子科学与技术（可授工学、理学学位）] 08[工学] 

基　　金：Conselho Nacional de Desenvolvimento Cientifico e Tecnologico [456744/2014-2  307686/2014-0] 

主　　题：Number-theoretic transforms Fractional transforms Matrix functions Image encryption 

摘      要：In this paper, we introduce fractional number-theoretic transforms (FrNTT) based on matrix functions. In contrast to previously proposed FrNTT, our approach does not require the construction of any number-theoretic transform (NTT) eigenvectors set. This allows us to obtain an FrNTT matrix by means of a closed-form expression corresponding to a linear combination of integer powers of the respective NTT matrix. Fractional Fourier, Hartley, cosine and sine number-theoretic transforms are developed. We show that fast algorithms applicable to ordinary NTT can also be used to compute the proposed FrNTT. Furthermore, we investigate the relationship between fractional Fourier and Hartley number-theoretic transforms, and demonstrate the applicability of the proposed FrNTT to a recently introduced image encryption scheme.