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"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.
List of contents
1. Digital Signak and Digital Filters.- 1.1 Analog and Digital Signals.- 1.2 Time and Frequency Domains.- 1.3 z-Transforms.- 1.4 Digital Filters.- 1.5 Optimal Digital Filter Design Criteria.- Problems.- 2. Linear Systems.- 2.1 State-Space Descriptions.- 2.2 Transfer Matrices and Minimal Realization.- 2.3 SISO Linear Systems.- 2.4 Sensitivity and Feedback Systems.- Problems.- 3. Approximation in Hardy Spaces.- 3.1 Hardy Space Preliminaries.- 3.2 Least-Squares Approximation.- 3.3 Minimum-Norm Interpolation.- 3.4 Nevanlinna-Pick Interpolation.- Problems.- 4. Optimal Hankel-Norm Approximation and H?-Minimization.- 4.1 The Nehari Theorem and Related Results.- 4.3 System Reduction.- 4.4 H?-Minimization.- Problems.- 5. General Theory of Optimal Hankel-Norm Approximation.- 5.1 Existence and Preliminary Results.- 5.2 Uniqueness of Schmidt Pairs.- 5.3 The Greatest Common Divisor: The Inner Function ?I0(z).- 5.4 AAK's Main Theorem on Best Hankel-Norm Approximation.- Problems.- 6. H?-Optimization and System Reduction for MIMO Systems.- 6.1 Balanced Realization of MIMO Linear Systems.- 6.2 Matrix-Valued All-Pass Transfer Functions.- 6.3 Optimal Hankel-Norm Approximation for MIMO Systems.- Problems.- References.- Further Reading.- List of Symbols.
