The book provides theory and applications of the Fourier-Bessel (FB) decomposition. It includes separation of components of multi-component non-stationary signals by using the FB expansion. The relation between the frequency and the order of the FB expansion coefficients has been developed. The components which are disjoint in the frequency domain, can be separated using the FB coefficients. If the components are disjoint in the time-frequency domain, the time-order representation based on the FB expansion is used to separate the components. It also covers some of the real-time applications of the FB decomposition like speech formant separation, bat echolocation signal components separation, amplitude and frequency modulated (AM-FM) signal separation and segmentation of electroencephalogram (EEG) signal.

Written using clear and accessible language, this text provides detailed coverage of the core mathematical concepts underpinning signal processing. All the core areas of mathematics are covered, including generalized inverses, singular value decomposition, function representation, and optimization, with detailed explanations of how basic concepts in these areas underpin the methods used to perform signal processing tasks. A particular emphasis is placed on the practical applications of signal processing, with numerous in-text practice questions and real-world examples illustrating key concepts, and MATLAB programs with accompanying graphical representations providing all the necessary computational background. This is an ideal text for graduate students taking courses in signal processing and mathematical methods, or those who want to establish a firm foundation in these areas before progressing to more advanced study.