Time-Scale Synthesis for Locally Stationary Signals

Abstract

We develop a time-scale synthesis-based probabilistic approach for the modeling of locally stationary signals. Inspired by our previous work, the model involves zero-mean, complex Gaussian wavelet coefficients, whose distribution varies as a function of time by time dependent translations on the scale axis. In a maximum a posteriori approach, we propose an estimator for the model parameters, namely the timevarying scale translation and an underlying power spectrum. The proposed approach is illustrated on a denoising example. It is also shown that the model can handle locally stationary signals with fast frequency variations, and provide in this case very sharp time-scale representations more concentrated than synchrosqueezed or reassigned wavelet transform.Index Terms-Wavelet transform, time warping, probabilistic synthesis model * The first author performed this work while at I2M, Aix-Marseille Université, France.

Synthesis-based time-scale transforms for non-stationary signals

“…Some of the results presented in this paper were already sketched in [23]; we refer also to [24], where the AM-TW model and variants were analyzed in details.…”