New second order cyclostationary analysis and application to the detection and characterization of a runner׳s fatigue

Cyclostationarity (CS), as characteristic of signals, is a technique that offers diagnostic advantages for the analysis of failures, faults and disturbances which are related to a system being examined. The aim of this paper is to introduce the concept of CS for signals and to present possibilities of statistical resampling procedures for the estimation of second order statistics of such signals. The resampling methods treated in this paper are referred to as subsampling and moving block bootstrap (MBB). A description of these methods is presented and their applicability to CS simulated data is proved. The comparison between those two procedures shows that subsampling seems to be more efficient and more relevant than MBB. The subsampling-based CS analysis of biomechanical ground reaction force signals (GRF signals), coming from a high level professional runner, proves the second order cyclostationary (CS2) nature of the GRF signals. Moreover, it enables us to distinguish successfully the CS2 cyclic frequencies of the signals under consideration. Some new indicators based on the subsampling procedure are also proposed. This allows a better characterization and a full innovative description of the different fatigue states of a runner.