New Statistics of the Second-Order Chirp Cyclostationary Signals: Definitions, Properties and Applications

Abstract

The chirp-cyclostationary (CCS) process is the generalized form of the cyclostationary (CS) process and it can describe the nonstationary stochastic signal models more exactly in practical applications. Basically, the statistics of the CCS signals have been defined and studied based on the correlation function. However, when the measurement is chosen as the above defined statistics, the output of a linear-variant filter is a zero-power signal for any input pure CCS signal. This is a barrier to further analyze the properties of the filters by the second-order statistics. In this paper, firstly two new complementary correlation function-based statistics and their basic properties are proposed and discussed. These two new statistics are connected by the generalized cyclic Wiener-Khinchin theorem. Then, we examine that the output of the filter is non-zero power under these new measurements. Based on this, the theories about the matched filter and system identification are developed, whose advantages are analyzed in theory. Finally, by proposing the estimators to the two statistics via a single record, the advantages of the proposed statistics over the classical second-order statistics are examined by the communication signals and the electrocardiogram (ECG) signals.