Signal Processing and Systems Theory Selected Topics [Paperback]

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. 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.1. Digital Signak and Digital Filters.- 1.1 Analog and Digital Signals.- 1.1.1 Band-Limited Analog Signals.- 1.1.2 Digital Signals and the Sampling Theorem.- 1.2 Time and Frequency Domains.- 1.2.1 Fotirier Transforms and Convolutions on Three Basic Groups.- 1.2.2 Frequency Spectra of Digital Signals.- 1.3 z-Transforms.- 1.3.1 Properties of the z-Transform.- 1.3.2 Causal Digital Signals.- 1.3.3 Initial Value Problems.- 1.3.4 Singular ló>