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"Signal Processing and Systems Theory" is concerned with the§study of H-optimization for digital signal processing and§discrete-time control systems. The first three chapters§present the basic theory and standard methods in digital§filtering and systems from the frequency-domain approach,§followed by a discussion of the general theory of§approximation in Hardy spaces. AAK theory is introduced,§first for finite-rank operators and then more generally,§before being extended to the multi-input/multi-output§setting. This mathematically rigorous book is self-contained§and suitable for self-study. The advanced mathematical§results derived here are applicable to digital control§systems and digital filtering.