Nonuniform Sampling for Random Signals Bandlimited in the Linear Canonical Transform Domain

TL;DR

This paper investigates nonuniform sampling of random signals bandlimited in the linear canonical transform domain, proposing an approximate recovery method and analyzing the mean square error, supported by simulations.

Contribution

It introduces a novel approach linking nonuniform sampling in the LCT domain to uniform sampling via second order statistics, with an approximate recovery method and error analysis.

Findings

Nonuniform sampling in LCT domain is equivalent to uniform sampling in second order statistics.

Proposed an approximate recovery method for nonuniform sampled signals.

Validated theoretical results through simulations.

Abstract

In this paper, we mainly investigate the nonuniform sampling for random signals which are bandlimited in the linear canonical transform (LCT) domain. We show that the nonuniform sampling for a random signal bandlimited in the LCT domain is equal to the uniform sampling in the sense of second order statistic characters after a pre-filter in the LCT domain. Moreover, we propose an approximate recovery approach for nonuniform sampling of random signals bandlimited in the LCT domain. Furthermore, we study the mean square error of the nonuniform sampling. Finally, we do some simulations to verify the correctness of our theoretical results.