An interplay between parameter ( p, q )-Boas transform and linear canonical transform

In this paper, we define and study parameter (p, q)-Boas transform of a signal in linear canonical transform domain. Also, we define the complex signals associated with parameter (p, q)-Boas transform and linear canonical transform and prove the generalized Boas transform product theorem (an analog of Bedrosian’s theorem) in the linear canonical transform domain. Further, using a linear combination of a signal and its parameter (p, q)-Boas transform, we define a η-linear canonical Boas transform and study some of its properties. Finally, we propose some η-linear canonical complex signals and give analysis of their linear canonical transform spectrum and eigenfunction property.