This interdisciplinary book simultaneously deals with three selected fields. Specifically, it presents a joint framework with the unified quantum-mechanical theories of resonant scattering, spectroscopy, and signal processing. Both the standard and non-standard analyses are expounded by encompassing the key ingredient of the S- and R-matrices, variational principles, complex coordinate scaling, wave packet propagation, Fredholm determinants, finite-rank separable expansions, filter diagonalization, the Lanczos algorithm, and the Pad methodology. The highly developed mathematical theory of...