Rényi entropy based complexity estimation of nonstationary signals: doctoral thesis - Saulig, Nicoletta (N. Saulig ; Fakultet elektrotehnike i računarstva, 2015)
ABSTARCT: In signal processing applications, the analyst is often faced with the problem of signal components identification, originating from one or more sources. The presence of different components can be assessed by the detection of their time supports in the time-frequency plane. In this thesis, it is shown how the instantaneous number of components in a signal can be estimated using the time-frequency Rényi entropy. Unlike the global entropy estimation, which is limited to signals with components being copies of a reference component that must be known to the user, the local Rényi entropy estimation is not limited to particular signal classes nor it requires prior knowledge of the signal. Using one of the most popular time-frequency distributions, the spectrogram, this thesis proves the local applicability of the counting property of the Rényi entropy in practical applications. The problem of quantifying the signal information content, i.e. the number of its components, in the case of components with unequal amplitudes, is addressed by a refined estimation algorithm. The algorithm allows the detection of the time supports of the spectral components, providing important information for components extraction methods. More complex cases are also analyzed, including signals with intersecting components in the time-frequency plane. The features of the local Rényi entropy estimations are found to be valid indicators of components crossings, with the potential use as a criterion in adaptive optimization of non-strictly positive time-frequency distributions. The results obtained by the local Rényi entropy estimation are shown to be valuable input information in blind source separation and classification procedures as well. -