Inversion formula for the windowed linear canonical transform

Abstract

We study the inversion formula for recovering a signal from its windowed linear canonical transform. Different from the known inversion formula, where a double integral is invoked, we show that every signal can be recovered from its windowed linear canonical transform with a univariate integral. Moreover, we show that the integral involved is convergent almost everywhere on $\mathbb{R}$ as well as in $L^p(\mathbb{R})$ for all $1<p<\mathrm{\infty }$. Furthermore, we also obtain an inversion formula for functions in $L^1(\mathbb{R})$ with the method of Cesàro summability.

Keywords:

• Linear canonical transform
• windowed linear canonical transform
• LCT
• inversion formula

2010 Mathematics Subject Classification:

• 42C20

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China [grant numbers 11926342 and 11926343].