Synchrosqueezing and Multicomponent Signal Analysis

Many signals from the physical world, e.g. speech or physiological records, can be modelled as a sum of amplitude and frequency-modulated (AM/FM) waves often called modes. In the last few decades, there has been an increasing interest in designing new accurate representations and processing methods for these type of signals. Consequently, the retrieval of the components (or modes) of a multicomponent signal is a central issue in many audio processing problems. The most commonly used techniques to carry out the retrieval are time-frequency or time-scale based signal representations. For the former, spectrogram reassignment techniques, reconstruction based on minimization of the ambiguity function associated with the Wigner-Ville distribution, synchrosqueezing using the short time Fourier transform or Fourier ridges have all been successfully used. For the latter, i.e., time-scale representations, wavelet ridges have also proven to be very efficient, the emphasis is on the importance of the wavelet choice with regard to the ridge representation. Synchrosqueezing techniques have also been developed within the wavelet framework. The main difference between the short time Fourier and wavelet representations is that the latter is more demanding in terms of the frequency separation of high frequency components. In this talk, I will propose a new implementation for RCM following on from some ideas of the synchrosqueezing transform (SST) and then show how it enables us to find out a relevant non-uniform sampling set for the signal, i.e., pre- serving its essential frequency characteristics, and finally how it can be used for signal denoising.