Analytic spectrum as a tool for time-frequency signal analysis

Abstract

The report substantiates the concept of the analytic spectrum and the synthesis of time-frequency representations of signals based on it. A number of properties of the analytic spectrum are considered and their comparison with the corresponding properties of the analytic signal is carried out. On the basis of this comparison, key features of similarity and dissimilarity between these dual concepts are formulated. The report discusses the relation between the analytic spectra of the local past and local future of the signal with the Page and Levin instantaneous spectra concepts. The report also presents the relation of analytic spectra of the signal's local past and future with the popular quadratic cone-shaped (Zhao-Atlas-Marks) time-frequency representations.