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.