{"product_id":"advanced-topics-in-system-and-volker-pohl-9783642036385","title":"Advanced Topics in System and Signal Theory: A Mathematical Approach","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 .\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Volker Pohl,Holger Boche\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3642036384\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783642036385\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 10\/16\/2009\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 241\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.17lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.63d","brand":"Volker Pohl","offers":[{"title":"Hardcover","offer_id":47579927150847,"sku":"9783642036385","price":109.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_82250f86-fc09-4ab0-81ce-a738caeec629.jpg?v=1763877626","url":"https:\/\/www.whiterainbookhouse.com\/products\/advanced-topics-in-system-and-volker-pohl-9783642036385","provider":"WR Book House","version":"1.0","type":"link"}