Advanced Topics in System and Signal Theory: A Mathematical Approach

di Volker Pohl (Autore)

Holger Boche (Autore)

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 2009

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 .

• Autore: Volker Pohl, Holger Boche
• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Collana: Foundations in Signal Processing, Communications and Networking
• Anno: 2009
• Rilegatura: Hardback
• Pagine: 241 p.
• Dimensioni: 235 x 155 mm
• EAN: 9783642036385

Testo in English