Advanced topics in system and signal theory : a mathematical approach / Volker Pohl, Holger Boche.
"The requirement of causality in system theory is inevitably accompanied by the appearance of certain mathematical operations, namely the Riesz proj- tion,the Hilberttransform,andthespectralfactorizationmapping.Aclassical exampleillustratingthisisthedeterminationoftheso-called Wiener?lter(the l...
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|---|---|
| Other Authors: | |
| Format: | Ebook |
| Language: | English |
| Published: |
Heidelberg ; New York :
Springer,
c2009.
|
| Series: | Foundations in signal processing, communications and networking ;
v. 4. |
| Subjects: | |
| Online Access: | Springer eBooks |
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| 100 | 1 | |a Pohl, Volker. |9 1082479 | |
| 245 | 1 | 0 | |a Advanced topics in system and signal theory : |b a mathematical approach / |c Volker Pohl, Holger Boche. |
| 260 | |a Heidelberg ; |a New York : |b Springer, |c c2009. | ||
| 300 | |a 1 online resource (viii, 241 p.)) : |b ill. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Foundations in signal processing, communications and networking ; |v v. 4. | |
| 500 | |a Description based on print version record. | ||
| 504 | |a Includes bibliographical references (p. 237-241). | ||
| 505 | 0 | 0 | |t Mathematical Preliminaries: -- |t Part I Mathematical Preliminaries: -- |t Function Spaces and Operators -- |t Fourier Analysis and Analytic Functions -- |t Banach Algebras -- |t Signal Models and Linear Systems -- |t Fundamental Operators: -- |t Part II Fundamental Operators: -- |t Poisson Integral and Hilbert Transformation -- |t Causal Projections -- |t Causality Aspects in Signal and System Theory: -- |t Part III Causality Aspects in Signal and System Theory: -- |t Disk Algebra Bases -- |t Causal Approximations -- |t On Algorithms for Calculating the Hilbert Transform -- |t Spectral Factorization. |
| 520 | |a "The requirement of causality in system theory is inevitably accompanied by the appearance of certain mathematical operations, namely the Riesz proj- tion,the Hilberttransform,andthespectralfactorizationmapping.Aclassical exampleillustratingthisisthedeterminationoftheso-called Wiener?lter(the linear, minimum means square error estimation ?lter for stationary stochastic sequences [88]). If the ?lter is not required to be causal, the transfer function of the Wiener ?lter is simply given by H(?)=? (?)/? (?),where ? (?) xy xx xx and ? (?) are certain given functions. However, if one requires that the - xy timation ?lter is causal, the transfer function of the optimal ?lter is given by 1 ? (?) xy H(?)= P ,?? (??,?] . + [? ] (?) [? ] (?) xx + xx? Here [? ] and [? ] represent the so called spectral factors of ? ,and xx + xx? xx P is the so called Riesz projection. Thus, compared to the non-causal ?lter, + two additional operations are necessary for the determination of the causal ?lter, namely the spectral factorization mapping ? ? ([? ] ,[? ] ),and xx xx + xx? the Riesz projection P ."--Publisher's website. | ||
| 538 | |a Mode of access: World Wide Web. | ||
| 588 | |a Automated GMD conversion. | ||
| 650 | 0 | |a Signal processing |x Mathematics |9 371288 | |
| 650 | 0 | |a System theory |x Mathematics |9 728316 | |
| 700 | 1 | |a Boche, Holger. |9 1082480 | |
| 830 | 0 | |a Foundations in signal processing, communications and networking ; |v v. 4. |9 1082481 | |
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