Advanced Topics in System and Signal Theory - A Mathematical Approach (Paperback, 2010 ed.)

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 .

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Foundations in Signal Processing, Communications and Networking, 4
Release date:	March 2012
First published:	March 2012
Authors:	Volker Pohl • Holger Boche
Dimensions:	235 x 155 x 13mm (L x W x T)
Format:	Paperback
Pages:	241
Edition:	2010 ed.
ISBN-13:	978-3-642-26096-4
Categories:	Books > Science & Mathematics > Mathematics > Numerical analysis Books > Computing & IT > General theory of computing > General Books > Computing & IT > Computer communications & networking > General Books > Computing & IT > Internet > Network computers Books > Computing & IT > Applications of computing > General Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematics for scientists & engineers Books > Professional & Technical > Electronics & communications engineering > Communications engineering / telecommunications > General
LSN:	3-642-26096-9
Barcode:	9783642260964

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