Parameterised time-frequency analysis methods and their engineering applications: A review of recent advances

It is well known that time-frequency analysis (TFA) characterises signals in time-frequency plane. Theoretically, traditional non-parameterised TFA can analyze any signal, but it is unable to provide the best representation for complex signals. On the other hand, parameterised TFAs provide a better representation of signal by parameterising kernel functions using additional parameters. Recently, parameterised TFAs have attracted widespread attention. In this paper, we first briefly revisit non-parameterised TFAs, then further discuss adaptive TFAs developed from non-parameterised TFAs, and then review four types of recent parameterised TFAs: Warped TFAs, Chirplet transforms, parameterised atomic decomposition, and parameterised TFA affine. From underlying principles and implementation point of view, we introduced the relationships, advantages and disadvantages of different types of parameterised TFAs. At the same time, we summarized the application of parameterised TFA in various fields and discussed research directions and trends in parameterised TFA study. This review focuses on a class of methods in TFA, parameterised TFA, summarizing its latest research progress and related engineering applications, so as to provide reference and guidance for researchers applying parametric TFA in different fields.