Advanced topics in system and signal theory : a mathematical approach /
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| Author / Creator: | Pohl, Volker. |
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| Imprint: | Berlin ; Heidelberg : Springer-Verlag, c2010. |
| Description: | 1 online resource. |
| Language: | English |
| Series: | Foundations in Signal Processing, Communications and Networking Foundations in Signal Processing, Communications and Networking. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/8891007 |
| Summary: | 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 . |
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| Physical Description: | 1 online resource. |
| Bibliography: | Includes bibliographical references. |
| ISBN: | 9783642036392 3642036392 |