Generalized spectrum analysis of Chirp Cyclostationary signals associate with linear canonical transform

Abstract

A chirp cyclostationary (CCS) process is a nonstationary stochastic process, whose statistics have been defined and utilized in radar and communication signal processing. However, spectrum analysis of CCS signals, which provides a spectral view to characterize a signal, has not been performed. Classical spectrum analysis is based on the Fourier transform, which is not suitable for CCS signals because of the multiplicative chirp signals in a CCS model. In this study, we propose a generalized spectral representation of chirp cyclostationary signals associated with a linear canonical transform. The proposed representation shows that a CCS signal can be represented by a linear combination of a series of jointly stationary and equal-bandwidth processes, which bridge the nonstationary and stationary processes. Furthermore, the relationships between the second-order statistics of the CCS process and its stationary representations are introduced. Finally, based on the above observations, a linear time-varying Wiener filter was designed for CCS signal denoising and time-varying channel estimation. Finally, the relationships between the nonstationarity of the input and output and time-varying properties of the systems are discussed, which are helpful for determining the nonstationarity of the outputs or the time-varying property of a system.