"Signal Processing and Systems Theory" is concerned with thestudy of H-optimization for digital signal processing anddiscrete-time control systems. The first three chapterspresent the basic theory and standard methods in digitalfiltering and systems from the frequency-domain approach, followed by a discussion of the general theory ofapproximation in Hardy spaces. AAK theory is introduced, first for finite-rank operators and then more generally, before being extended to the multi-input/multi-outputsetting. This mathematically rigorous book is self-containedand suitable for self-study. The advanced mathematicalresults derived here are applicable to digital controlsystems and digital filtering.