On Non-Symmetric Forms of Time-Varying Autocorrelation Function in the Analysis of Cyclostationary Processes

The paper is aimed at investigating the difference between different forms of time-varying autocorrelation function (TVACF) used for the quantitative expression of the second-order statistical properties exhibiting by non-stationary random processes. The generalized form of TVACF is proposed where the position of the current time moment can be set by means of additional parameter. The relation between the generalized form of TV ACF and its symmetric form is derived for the components of the corresponding cyclic autocorrelation function (CACF). Some invariant has been highlighted which does not depend on the form chosen for the process modelling or estimation. Some symmetry properties held by CACF are discussed. A pulse-amplitude modulated process is considered as a modelled process which sets up an illustrative example which helps to show the visual difference between the correlation diagrams depicting three forms of TV ACF used most frequently in the research sources on cyclostationary analysis.