Higher order spectra analysis and applications
Loading...
Date
2024-04
Authors
Βέρρος, Θεοφάνης-Δημήτριος
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
This Master’s thesis, with title “Higher Order Spectra Analysis and Applications”, has its motivation on the techniques that can be used to derive additional information with the use of Higher-Order Spectra in the field of digital signal processing and analysis. Here will be presented the ways that cumulants and in general higher order statistics provide advantages for the study of signals. We will place our application focus on the bispectrum of different signals, which
refers to the Fourier transform of the third-order spectrum. We want to determine the information we can get from that procedure, what are the expectations we mathematically have and the exact results we get. Why do we receive the results we do and how is phase-coupling resulting in every case. Our approach will be done on sinusoid signals of different frequencies and random phases, altered by being summed up together and/or passed through quadratic and
cubic non-linearities. By those procedures, we are given different results, and, in every case, we can name different information about the signals. Although this procedure may sound simplified, it can give us a better understanding
of how this theory can be applied in everyday life research, sensors, and medical tools. Therefore, it was of high importance for us to test how the theory applies and gain knowledge on how it can be properly used. The techniques involved and all the mathematical principles are being explored and explained in the scope of this thesis. Additionally, the reasons on why, how and where higher order spectra prove superior over the estimation of the power spectral density or simply the power spectrum of discrete-time deterministic or stochastic signals. Power spectral density estimates have proved useful in the creation of multiple tools we use every day. Nevertheless, we investigated and present that in particular situations we have to look beyond the power spectrum of a signal to extract information, in regard to deviations from Gaussianity and in presence of phase relations. Closing, our approach as stated can be considered simplistic, nevertheless it carries out proof on how these methods work. Our conclusions show what our theoretical approach predicts and it is explaining how everything is derived from our initial signals.
Description
Keywords
Spectra analysis, Bispectrum