A reformulation of weighted fractional Fourier transform

被引：6
|
作者：
Zhao, Tieyu [1 ]
Yuan, Lin [2 ]
Li, Mingwei [1 ]
Chi, Yingying [1 ]
机构：
[1] Northeastern Univ Qinhuangdao, Informat Sci Teaching & Res Sect, Qinhuangdao 064000, Hebei, Peoples R China
[2] Zhejiang Normal Univ, Coll Math & Comp Sci, Jinhua 321004, Zhejiang, Peoples R China
来源：
DIGITAL SIGNAL PROCESSING | 2020年 / 104卷
基金：
中国国家自然科学基金;
关键词：
Signal processing; Fractional Fourier transform; Weighted fractional Fourier transform; Image encryption; Computational complexity; PERMUTATION;
D O I：
10.1016/j.dsp.2020.102807
中图分类号：
TM [电工技术]; TN [电子技术、通信技术];
学科分类号：
0808 ; 0809 ;
摘要：
This paper investigates a class of weighted-type fractional Fourier transform (WFRFT), which is mainly used in signal processing and image encryption. To date, studies have primarily focused on the application of WFRFT, and few studies have examined its properties in detail. We propose a new reformulation of WFRFT, whose properties can be readily proven. Multiweighted-type fractional Fourier transform (M-WFRFT) has attracted researchers' attention as a generalized form of WFRFT. It is very difficult to prove the properties of M-WFRFT in weighted form, and researchers have assumed that M-WFRFT has the properties of WFRFT in application. The properties of M-WFRFT are proved by applying the new reformulation proposed. The results show that M-WFRFT has boundary and unitary properties, but in few cases. We analyze and discuss the conditions in which that M-WFRFT satisfies the boundary and unitary conditions, providing a theoretical foundation for application of M-WFRFT. (C) 2020 Elsevier Inc. All rights reserved.
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页数：18
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