UID:
almahu_9949199242202882
Format:
XIII, 261 p.
,
online resource.
Edition:
2nd ed. 1997.
ISBN:
9783642591457
Series Statement:
Springer Series in Information Sciences ; 26
Content:
Discrete H¿ Optimization 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 mathermatical results derived here are applicabel to digital control systems and digital filtering.
Note:
1. Digital Signals 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 -- 4.2 s-Numbers and Schmidt Pairs -- 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.
In:
Springer Nature eBook
Additional Edition:
Printed edition: ISBN 9783540619598
Additional Edition:
Printed edition: ISBN 9783642591464
Language:
English
DOI:
10.1007/978-3-642-59145-7
URL:
https://doi.org/10.1007/978-3-642-59145-7
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