Sampling theorems and error estimates for random signals in the linear canonical transform domain

• A uniform sampling theorem for a random signal bandlimited in the LCT domain is studied in this paper.
• A multi-channel sampling theorem for a random signal bandlimited in the LCT domain is also formulated.
• Two kinds of reconstruction error estimates (aliasing error and truncation error) for uniformly sampling a random signal in the LCT domain are analyzed.

The linear canonical transform (LCT) plays an important role in optical and digital signal processing. Over the past few decades, there has been a vast amount of research on sampling theorems for a deterministic signal bandlimited in the LCT domain. However, signals are usually random in practical situations. Hence in this paper, we study sampling theorems for a random signal bandlimited in the LCT domain. We first construct a random signal theoretic framework in the LCT domain, such as the LCT power spectral density and the LCT auto-correction function. Then, we formulate uniform sampling theorem and multi-channel sampling theorem for a random signal bandlimited in the LCT domain. Finally, we analyze two kinds of reconstruction error estimates for uniformly sampling a random signal in the LCT domain: aliasing error and truncation error.