Advanced Topics in System and Signal Theory
Hardcover
Rs 8160
Currently out of stock.
Request this book.| Genre: | Computer Science |
|---|---|
| Language : | English |
| Published: | October 16, 2009 |
| Edition: | 7th |
Hardcover | |
| ISBN13: | 9783642036385 |
| ISBN10: | 3642036384 |
| Dimensions: | 6.25 x 9.25 x 0.75 inches |
| Weight: | 1 g |
About the Book
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 .