A new music-empirical wavelet transform methodology for time-frequency analysis of noisy nonlinear and non-stationary signals

The goal of signal processing is to estimate the contained frequencies and extract subtle changes in the signals. In this paper, a new adaptive multiple signal classification-empirical wavelet transform (MUSIC-EWT) methodology is presented for accurate time-frequency representation of noisy non-stationary and nonlinear signals. It uses the MUSIC algorithm to estimate the contained frequencies in the signal and build the appropriate boundaries to create the wavelet filter bank. Then, the EWT decomposes the time-series signal into a set of frequency bands according to the estimated boundaries. Finally, the Hilbert transform is applied to observe the evolution of calculated frequency bands over time. The usefulness and effectiveness of the proposed methodology are validated using two simulated signals and an ECG signal obtained experimentally. The results demonstrate clearly that the proposed methodology is immune to noise and capable of estimating the optimal boundaries to isolate the frequencies from noise and estimate the main frequencies with high accuracy, especially the closely-spaced frequencies.