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Item Details
| Title:
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ADVANCED TOPICS IN SYSTEM AND SIGNAL THEORY
A MATHEMATICAL APPROACH |
| By: |
Volker Pohl, Holger Boche |
| Format: |
Paperback |
| List price:
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£109.99 |
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further information.
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| ISBN 10: |
3642260969 |
| ISBN 13: |
9783642260964 |
| Publisher: |
SPRINGER-VERLAG BERLIN AND HEIDELBERG GMBH & CO. KG |
| Pub. date: |
25 February, 2012 |
| Edition: |
2010 ed. |
| Series: |
Foundations in Signal Processing, Communications and Networking 4 |
| Pages: |
241 |
| Description: |
In an in-depth analysis of selected methods in signal and system theory that apply to problems in communications, stochastic processes and optimal filter theory, the authors take a functional analysis and operator theoretic approach to linear system theory |
| Synopsis: |
The requirement of causality in system theory is inevitably accompanied by the appearance of certain mathematical operations, namely the Riesz proj- tion,theHilberttransform,andthespectralfactorizationmapping.Aclassical exampleillustratingthisisthedeterminationoftheso-calledWiener?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 . |
| Illustrations: |
5 Illustrations, black and white; VIII, 241 p. 5 illus. |
| Publication: |
Germany |
| Imprint: |
Springer-Verlag Berlin and Heidelberg GmbH & Co. K |
| Returns: |
Returnable |
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