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Books > Computing & IT > Computer communications & networking
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Advanced Topics in System and Signal Theory - A Mathematical Approach (Hardcover, 2010 ed.)
Loot Price: R3,156
Discovery Miles 31 560
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Advanced Topics in System and Signal Theory - A Mathematical Approach (Hardcover, 2010 ed.)
Series: Foundations in Signal Processing, Communications and Networking, 4
Expected to ship within 10 - 15 working days
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Total price: R3,176
Discovery Miles: 31 760
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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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