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.
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| Series: | Foundations in signal processing, communications and networking ;
v. 4. |
| Subjects: | |
| Online Access: | Springer eBooks |
| Summary: | "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. |
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| Item Description: | Description based on print version record. |
| Physical Description: | 1 online resource (viii, 241 p.)) : ill. |
| Format: | Mode of access: World Wide Web. |
| Bibliography: | Includes bibliographical references (p. 237-241). |
| ISBN: | 1282459422 3642036392 (Internet) 3642036392 9781282459427 9783642036392 (Internet) 9783642036392 |