A reformulation of weighted fractional Fourier transform

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.