Sampling of bandlimited signals in the linear canonical transform domain

Abstract

The linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing. This paper investigates the sampling of bandlimited signals in LCT domain. First, we propose the linear canonical series (LCS) based on the LCT, which is a generalized pattern of Fourier series. Moreover, the LCS inherits all the nice properties from the LCT. Especially, the Parseval’s relation is presented for the LCS, which is used to derive the sampling theorem of LCT. Then, utilizing the generalized form of Parseval’s relation for the complex LCS, we obtain the sampling expansion for bandlimited signals in LCT domain. The advantage of this reconstruction method is that the sampling expansion can be deduced directly not based on the Shannon theorem.