9783642260964 - Advanced Topics in System and Signal Theory: A Mathematical Approach (Foundations in Signal Processing, Communications and Networking, Band 4) von Pohl, Volker; Boc... (4 Ergebnisse)

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Taschenbuch. Zustand: Neu. Advanced Topics in System and Signal Theory | A Mathematical Approach | Volker Pohl (u. a.) | Taschenbuch | Foundations in Signal Processing, Communications and Networking | viii | Englisch | 2012 | Springer | EAN 9783642260964 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 .