  This paper deals with the modeling of non-stationary signals, from the point
of view of signal synthesis. A class of random, non-stationary signals,
generated by synthesis from a random timescale representation, is introduced
and studied. Non-stationarity is implemented in the timescale representation
through a prior distribution which models the action of time warping on a
stationary signal. A main originality of the approach is that models directly a
timescale representation from which signals can be synthesized, instead of
post-processing a pre-computed timescale transform. A maximum a posteriori
estimator is proposed for the time warping parameters and the power spectrum of
an underlying stationary signal, together with an iterative algorithm, called
JEFAS-S, for the estimation, based upon the Expectation Maximization approach.
Numerical results show the ability of JEFAS-S to estimate accurately time
warping and power spectrum. This is in particular true when time warping
involves fast variations, where a similar approach called JEFAS, proposed
earlier, fails. In addition, as a by-product, the approach is able to yield
extremely sharp timescale representations, also in the case of fast varying
non-stationarity, where standard approaches such as synchrosqueezing fail.
