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Advanced Topics in System and Signal Theory: A Mathematical Approach 2010 Edition
Contributor(s): Pohl, Volker (Author), Boche, Holger (Author)

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 ISBN: 3642036384     ISBN-13: 9783642036385
Publisher: Springer
OUR PRICE: $104.49  

Binding Type: Hardcover - See All Available Formats & Editions
Published: October 2009
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Additional Information
BISAC Categories:
- Mathematics | Applied
- Technology & Engineering | Telecommunications
- Computers | Networking - Hardware
Dewey: 621.382
LCCN: 2009934791
Series: Foundations in Signal Processing, Communications and Networking
Physical Information: 0.63" H x 6.14" W x 9.21" L (1.17 lbs) 241 pages
Features: Bibliography, Illustrated, Table of Contents
 
Descriptions, Reviews, Etc.
Publisher Description:
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 .
 
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