Research of stationary partitions in nonstationary processes by measurement of spectral distance with the help of nondyadic Malvar's decomposition

In this article, we propose a simple algorithm allowing the research of stationary partitions in locally stationary processes, by use of adapted local bases like the local DCT or the short-time Fourier transform. The algorithm aims at finding some windows of which width is adapted to the rate of change in the spectrum. A similar approach was proposed by Adak (1995), who detected changes over time in the spectra of the process to select a data-dependent window size. The same principle is used in our algorithm, with a more robust estimation of the difference in spectra than Adak. After denoising of the periodogram with the help of the undecimated wavelet transform, we consider the "symmetrical case" in the best partition selection method. A post-treatment permits us to deal with the nonuniform partitions.