This is a Tutorial of data-driven time-frequency analysis methods.

Introduction

Non-stationary signal processing methods have developed a lot. One way is the linear time-frequency transforms that includes short time Fourier transform, wavelet transform, Stockewell transform(@Stockwell1996) etc. A downside of linear transforms is that the atoms are fixed and predetermined. The time- frequency distribution is blurred due to the Heisenberg uncertainty principle.

One other way started in the late nineties when Huang et al. proposed the empirical mode decomposition(EMD)(@emd), which extracts intrinsic mode functions from the input signal recursively using sifting processing. The EMD method has been widely used in many areas despite its shortage of a consolidate theoretical background. To overcome that difficulty, some other methods have been proposed, such as synchrosqueezing wavelet transform(@daubechies), synchrosqueezing Fourier transform, empirical wavelet transform, singular spectrum analysis(SSA), variational mode decomposition(VMD) etc.

While efforts to develop fully data driven yet mathematically sound algorithms for signal decompositon and TF analysis of nonstationary data continume to grow, there has been a lot of interest in extending existing data driven approaches to process nonstationary multidimensional and multivariate data sets.

References