Advanced Spectral Analysis with Applications

Abstract: Spectral analysis has advanced the last decades as a signal processing tool to extract significant information about certain properties of measured data. The practical use of spectral analysis techniques in time-series analysis has been emphasized in the immense amount of previous literature in the field and by a rapidly growing number of applications. In this thesis, a variety of spectral analysis techniques are presented which address some fundamental problems in signal processing. The proposed methods are accompanied by several experimental and simulated data examples showing the advantages of the suggested approaches.The concept of spectral analysis is briefly introduced along with a condensed presentation of the area of magnetic resonance spectroscopy (MRS), which is an application area treated in several parts of the thesis. The technical contributions include several methods for frequency-selective analysis of exponentially damped sinusoidal signals, invocation of prior knowledge about the signal parameter relations in MRS multiplets for improved parametric spectral estimation, theoretical expressions for the lower error bounds on estimated signal parameters for damped sinusoidal components in the frequency-selective analysis framework, multichannel spectral analysis of MRS data, area-selective spectral analysis of two-dimensional data, spectral smoothing via cepstrum thresholding in one and two dimensions, and spectral analysis of irregularly sampled data.The majority of the presented techniques for magnetic resonance spectroscopy data are parametric methods where a certain amount of prior knowledge about the signal of interest is required, but alternative semi-parametric and non-parametric approaches are also suggested for some of the considered problems. The suggested cepstrum thresholding-based methods are non-parametric, and the analysis on unevenly sampled data contains a set of both non-parametric and parametric approaches.