Volker Pohl

(Author)

Advanced Topics in System and Signal Theory: A Mathematical Approach (2010)Paperback - 2010, 14 March 2012

Advanced Topics in System and Signal Theory: A Mathematical Approach (2010)
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Part of Series
Foundations in Signal Processing, Communications and Network
Print Length
241 pages
Language
English
Publisher
Springer
Date Published
14 Mar 2012
ISBN-10
3642260969
ISBN-13
9783642260964

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

Product Details

Authors:
Volker PohlHolger Boche
Book Edition:
2010
Book Format:
Paperback
Country of Origin:
NL
Date Published:
14 March 2012
Dimensions:
23.39 x 15.6 x 1.35 cm
ISBN-10:
3642260969
ISBN-13:
9783642260964
Language:
English
Location:
Berlin, Heidelberg
Pages:
241
Publisher:
Weight:
358.34 gm

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