NON-STATIONARY SIGNALS: PHASE-ENERGY APPROACH––THEORY AND SIMULATIONS

Modern time–frequency methods are intended to deal with a variety of non-stationary signals. One specific class, prevalent in the area of rotating machines, is that of harmonic signals of varying frequencies and amplitude. This paper presents a new adaptive phase-energy (APE) approach for time–frequency representation of varying harmonic signals. It is based on the concept of phase (frequency) paths and the instantaneous power spectral density (PSD). It is this path which represents the dynamic behaviour of the system generating the observed signal. The proposed method utilises dynamic filters based on an extended Nyquist theorem, enabling to extract signal components with optimal signal-to-noise ratio. The APE detects the most energetic harmonic components (frequency paths) in the analysed signal. Tests on simulated signals show the superiority of the APE in resolution and resolving power as compared to STFT and wavelets wave-packet decomposition. The dynamic filters also enable the reconstruction of the signal components (paths) from the noisy signal. A quantitative comparison was performed both for the detected path in the time–frequency plane as well as for the reconstructed signal, demonstrating the performance of the APE.