{"product_id":"advanced-topics-in-system-and-signal-theory-a-mathematical-approach-9783642036385","title":"Advanced Topics in System and Signal Theory: A Mathematical Approach","description":"\u003cp\u003e • Author(s): Volker Pohl | Holger Boche\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Applied\u003c\/p\u003e\u003cp\u003eThe 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 .\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Hardcover","offer_id":47609114755223,"sku":"9783642036385","price":11297.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783642036385.webp?v=1775056413","url":"https:\/\/atlanticbooks.com\/products\/advanced-topics-in-system-and-signal-theory-a-mathematical-approach-9783642036385","provider":"Atlantic Books","version":"1.0","type":"link"}