EMD-based time-frequency analysis methods of audio signals

Using appropriate signal processing tools to analyze time series data accurately is essential for correctly interpreting the underlying processes. Commonly employed methods include kernel-based transforms that utilize base functions and modifications to depict time series data. This paper refers to the analysis of audio data using two such transforms: the Fourier transform and the wavelet transform, both based on assumptions regarding the signal's linearity and stationarity. However, in audio engineering, these assumptions often do not hold as the statistical characteristics of most audio signals vary over time, making them unsuitable for treatment as outputs from a Linear Time-Invariant (LTI) system. Consequently, more recent methods have shifted towards breaking down signals into various modes in an adaptive, data-specific manner, potentially offering benefits over traditional kernel-based methods. Techniques like empirical mode decomposition and Holo-Hilbert Spectral Analysis are examples of this. The effectiveness of these methods was tested through simulations using speech signals for both kernel-based and adaptive decomposition methods, demonstrating that these adaptive methods are effective for analyzing audio data that is both nonstationary and an output of the nonlinear system.