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pohl v advanceics system signal theory 2009

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Textbook in PDF format This monograph is intended primarily for engineers working on such robustness problems under a causality constraint. At the beginning, it presents the mathematical methods, necessary to approaching these problems. Then some related classical results concerning the boundedness and continuity of the Hilbert transform and Riesz projection are presented. Finally, these methods and results are applied to selected topics from signal processing. The first part of the this monograph gives a very brief introduction to the main mathematical methods used later in the book. This part serves primarily as a review of results needed in later chapters, so that the work becomes essentially self-contained. The different topics are only covered as far as they will be needed and proofs are sometimes omitted. Appropriate reference are given for those who want a more detailed introduction to the different topics. This work presupposes a working knowledge of real and complex analysis (roughly as contained in [70]) as well as some basic elements of functional analysis (e.g. as in [54]). The second part collects the basic abstract results concerning the continuity and the boundedness of the Hilbert transform and the Riesz projection on different Banach spaces. These results are the basis for the applications discussed in the third part of this monograph. Here four applications from signal processing are investigated in some detail, namely the expansions of transfer functions in orthonormal bases in Chapter 7, the linear approximation from measured data in Chapter 8, the calculation of the Hilbert transform in Chapter 9, and the spectral factorization in Chapter 10_. All these topics are essentially problems of recovery or approximation of causal function from measured data, which are generally corrupted by small errors. It is investigated how these errors influence the possibility of recovering the desired signal from the measurements under the restriction that this recovery is based only on past and present measurements, i.e. under the requirement of causality. Mathematical Preliminaries. Function Spaces and Operators. Fourier Analysis and Analytic Functions. Banach Algebras. Signal Models and Linear Systems. Fundamental Operators. Poisson Integral and Hilbert Transformation. Causal Projections. Causality Aspects in Signal and System Theory. Disk Algebra Bases. Causal Approximations. On Algorithms for Calculating the Hilbert Transform. Spectral Factorization

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pohl v advanceics system signal theory 2009