Buch, Englisch, 241 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 388 g
Reihe: Foundations in Signal Processing, Communications and Networking
A Mathematical Approach
Buch, Englisch, 241 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 388 g
Reihe: Foundations in Signal Processing, Communications and Networking
ISBN: 978-3-642-26096-4
Verlag: Springer
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
I Mathematical Preliminaries.- Function Spaces and Operators.- Fourier Analysis and Analytic Functions.- Banach Algebras.- Signal Models and Linear Systems.- II Fundamental Operators.- Poisson Integral and Hilbert Transformation.- Causal Projections.- III Causality Aspects in Signal and System Theory.- Disk Algebra Bases.- Causal Approximations.- On Algorithms for Calculating the Hilbert Transform.- Spectral Factorization.
