New convolution related theorems and applications associated with offset linear canonical transform
Gita Rani Mahato, Sarga Varghese, Manab Kundu
TL;DR
The paper develops new convolution and correlation theorems for the offset linear canonical transform (OLCT) and analyzes related spectral results. It introduces OLCT-specific convolution and correlation definitions, derives their fundamental properties, and establishes real Paley-Wiener and Boas-type theorems in the OLCT domain. Potential applications in multiplicative OLCT-based filter design for signal recovery in optics and signal processing are discussed. The results extend the OLCT toolkit and suggest further study in $L^p$ and Schwartz-type spaces.
Abstract
In this paper, we define new type of convolution and correlation theorems associated with the offset linear canonical transform (OLCT). Additionally, we discuss their applications in multiplicative filter design, which may prove useful in optics and signal processing for signal recovery. Furthermore, we explore the real Paley-Wiener (PW) and Boas theorems for the OLCT, analyzing signal characteristics for OLCT within the L2 domain.