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Wir sind gerne für Sie daThe 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.
Produkteigenschaften
- Artikelnummer: 9783642260964
- Medium: Buch
- ISBN: 978-3-642-26096-4
- Verlag: Springer
- Erscheinungstermin: 14.03.2012
- Sprache(n): Englisch
- Auflage: 2010
- Serie: Foundations in Signal Processing, Communications and Networking
- Produktform: Kartoniert, Previously published in hardcover
- Gewicht: 388 g
- Seiten: 241
- Format (B x H x T): 155 x 235 x 14 mm
- Ausgabetyp: Kein, Unbekannt