Signal Stationarity Estimation with Matlab

Estimation whether a given signal is wide-sense stationarity using a novel method.

The presented codes are two Matlab functions for wide-sense stationarity (WSS) estimation of a signal (e.g., time series) using a novel method developed in two variants. The first variant uses a statistical inference approach (for instance, it implements the Wilcoxon rank sum test and the Brown-Forsythe test), while the second one is purely empirical – it estimates the WSS of the signal "as it is" via comparison of its time-localized summary statistics (mean, variance, covariance), without any assumptions about the underlying process or the population.

The functions provide a computation of four Boolean flags for:

1) overall wide-sense stationarity i.e., simultaneous stationarity about mean, variance and autocovariance;

2) stationarity about the mean;

3) stationarity about the variance (and hence about the RMS-value);

4) time-invariance of the autocovariance (and hence of the autocorrelation and PSD).

A few examples are given to clarify the usage of the functions. For convenience, the input and output arguments are given at the beginning of each function.

The codes are based on the theory described in:

[1] H. Zhivomirov, I. Nedelchev. A Method for Signal Stationarity Estimation. Romanian Journal of Acoustics and Vibration, ISSN: 1584-7284, Vol. XVII, No. 2, pp. 149-155, 2020. (http://rjav.sra.ro/index.php/rjav/article/view/178/103).

[2] H. Zhivomirov. An Empirical Method for Signal Stationarity Estimation. The Scientific Bulletin, Series C: Electrical Engineering and Computer Science, ISSN: 2286-3540, Vol. 86, Issue 2, pp. 243-256, 2024. (https://www.scientificbulletin.upb.ro/rev_docs_arhiva/rezb81_132280).