A Power Variance Test for Nonstationarity in Complex-Valued Signals

TL;DR

This paper introduces an efficient algorithm for detecting nonstationarity in complex-valued signals by analyzing power variance, using bootstrap and FFT techniques, applicable to turbulent flow data.

Contribution

A novel, computationally efficient test for nonstationarity in complex signals that identifies various nonstationary behaviors using bootstrap and FFT methods.

Findings

Effective detection of nonstationarity in turbulent flow data

Algorithm runs in O(N log N) time, suitable for large datasets

Capable of identifying jumps and sinusoidal components

Abstract

We propose a novel algorithm for testing the hypothesis of nonstationarity in complex-valued signals. The implementation uses both the bootstrap and the Fast Fourier Transform such that the algorithm can be efficiently implemented in O(NlogN) time, where N is the length of the observed signal. The test procedure examines the second-order structure and contrasts the observed power variance - i.e. the variability of the instantaneous variance over time - with the expected characteristics of stationary signals generated via the bootstrap method. Our algorithmic procedure is capable of learning different types of nonstationarity, such as jumps or strong sinusoidal components. We illustrate the utility of our test and algorithm through application to turbulent flow data from fluid dynamics.