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Spectral analysis of nonstationary signals on a two dimensional space

This paper describes a method and its aliasing filtering for the analysis of nonstationary signals. A modulation model is firstly given to represent nonstationary signals. An instantaneous evaluation function is then defined at a single timepoint realising minimum data length responding to fast time variations. An instantaneous autocorrelation is given by instantaneous representation of time dependent autocorrelation. Secondly, the nonstationary spectrum is represented on a two dimensional (2-D) space with two frequency axes. These two axes are defined by the transformation of instantaneous autocorrelation signals from 2-D space with variables of lag and time. The first and the second axes correspond to stationary and nonstationary frequencies respectively. Band limitation of signals and sampling period on 2-D space are constrained to prevent aliasing caused by 2-D periodic sampling. In this analysis, signal, aliasing and sampling period are defined as instantaneous autocorrelation, error and calculation period for a time-dependent spectrum respectively. As the result of application, it was proved that the proposed method provides more useful and detailed knowledge compared to conventional analysis methods based on assuming stationary.