Advanced Topics in System and Signal Theory: A Mathematical Approach (Foundations in Signal Processing, Communications and Networking, 4)

Pohl, Volker; Boche, Holger

ISBN 10: 3642036384 / ISBN 13: 9783642036385

Edité par Springer, 2009

In. N° de réf. du vendeur ria9783642036385_new

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 .

Détails bibliographiques

Titre : Advanced Topics in System and Signal Theory:...
Éditeur : Springer
Date d'édition : 2009
Reliure : Couverture rigide
Etat : New