Recent Advances in Theory and Methods for Nonstationary Signal Analysis

All physical processes are nonstationary. When analyzing time series, it should be remembered that nature can be amazingly complex and that many of the theoretical constructs used in stochastic process theory, for example, linearity, ergodicity, normality, and particularly stationarity, are mathematical fairy tales. There are no stationary time series in the strict mathematical sense; at the very least, everything has a beginning and an end. Thus, while it is necessary to know the theory of stationary processes, one should not adhere to it dogmatically when analyzing data from physical sources, particularly when the observations span an extended period. Nonstationary signals are appropriate models for signals arising in several fields of applications including communications, speech and audio, mechanics, geophysics, climatology, solar and space physics, optics, and biomedical engineering. Nonstationary models account for possible time variations of statistical functions and/or spectral characteristics of signals. Thus, they provide analysis tools more general than the classical Fourier transform for finite-energy signals or the power spectrum for finite-power stationary signals. Nonstationarity, being a " nonproperty " has been analyzed from several different points of view. Several approaches that generalize the traditional concepts of Fourier analysis have been considered, including time-frequency, timescale , and wavelet analysis, and fractional Fourier and linear canonical transforms. Approaches that generalize the power-spectrum analysis include cyclostationary signal analysis, multitaper spectral estimation, and evolutionary spectral analysis. In addition, techniques such as adaptive system and signal analysis, empirical mode decomposition, and other data-driven methods have been used with the purpose of modeling nonstationary phenomena. In this special issue, recent advances in the theory and methodologies for nonstationary signal analysis are addressed, different approaches are compared, emerging or new techniques are proposed, and new application fields are explored. Of the 51 papers submitted, only 19 were accepted after the review process. Four papers are related to basic topics of nonstationary signal analysis such as instantaneous frequency estimation, time-frequency detection, Zak transform, and AM-FM analysis. In the paper " An efficient algorithm for instantaneous frequency estimation of nonstationary multicomponent signals in low SNR " by J. Lerga et al., a method for components instantaneous frequency (IF) estimation of multicomponent signals in low signal-to-noise ratio (SNR) is proposed. The method combines a new modification of a blind source separation algorithm for components separation, with the improved adaptive IF estimation procedure based on the modified sliding pairwise intersection of confidence intervals rule. In the paper " Time-frequency …