{"product_id":"advanced-topics-in-system-and-signal-theory-a-mathematical-approach-von-volker-pohl-holger-boche-1","title":"Advanced Topics in System and Signal Theory","description":"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 .\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783642260964\"\u003e\u003ch3\u003eA Mathematical Approach\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783642260964","offer_id":39428470046813,"sku":"9783642260964","price":106.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/4e538f82-32eb-4138-9c95-de59cdcb2455.jpg?v=1778134926","url":"https:\/\/shop.autorenwelt.de\/products\/advanced-topics-in-system-and-signal-theory-a-mathematical-approach-von-volker-pohl-holger-boche-1","provider":"Autorenwelt Shop","version":"1.0","type":"link"}