We study locally self-similar processes (LSSPs) in Silverman's sense. By
deriving the minimum mean-square optimal kernel within Cohen's class
counterpart of time-frequency representations, we obtain an optimal estimation
for the scale invariant Wigner spectrum (SIWS) of Gaussian LSSPs. The class of
estimators is completely characterized in terms of kernels, so the optimal
kernel minimizes the mean-square error of the estimation. We obtain the SIWS
estimation for two cases: global and local, where in the local case, the kernel
is allowed to vary with time and frequency. We also introduce two
generalizations of LSSPs: the locally self-similar chrip process and the
multicomponent locally self-similar process, and obtain their optimal kernels.
Finally, the performance and accuracy of the estimation is studied via
simulation.Comment: 28 page