Read e-book online Advances in Imaging and Electron Physics, Vol. 117 PDF

By Peter W. Hawkes

ISBN-10: 0120147599

ISBN-13: 9780120147595

Advances in Imaging and Electron Physics merges long-running serials-Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. The sequence beneficial properties prolonged articles at the physics of electron units (especially semiconductor devices), particle optics at low and high energies, microlithography, picture technological know-how and electronic picture processing, electromagnetic wave propagation, electron microscopy, and the computing tools utilized in most of these domain names.

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DOUGHERTY AND YIDONG CHEN It can be shown that (Chen and Dougherty, 1996) min P(S) P(N ) , 3 E[T ](b3 − c3 ) 3 − c b − a3 d3 ≤ E[e[r ]] ≤ max (62) P(N ) P(S) , 3 E[T ](b3 − c3 ) 3 − c b − a3 d3 The optimal Þlter has an error bounded by the expected steady-state error for the adaptive Þlter. For the special case D = 0, the two errors must agree because all Þlters whose parameters lie in the single recurrent class of the Markov chain have equal error. For D = 0, E[e[r ]] = E[T ]P(N ) b3 − c3 b3 − a 3 (63) In this section we have concentrated on steady-state analysis and ignored transient analysis.

In one, it is assumed there is a known point in the passband; in the other, no such assumption is made. The Þrst case requires more prior knowledge, possesses an analytic solution, and results in passband parameters having less variability in the steady state of the adaptation process. A. Granulometric Spectral Theory Given a Euclidean granulometry { is deÞned by t }, the size distribution of a compact set S (t) = ν[S] − ν[ t (S)] (80) The size distribution gives the volume of the set removed by t .

85) then (S ∪ N ) = ∞ [ t2k−1 (S k=1 ∪ N) − t2k (S ∪ N )] (86) This shows the bandpass nature of the Þlter. There are other decompositions of leading to error representations. For instance, if = [t1 , t2 ] ∪ . . ∪ [t2m+1 , t2m+2 ] (87) with t2m+2 < ∞, then the representation of Eq. (86) holds with m + 1 in place of ∞. Or, if = [t1 , t2 ] ∪ . . ∪ [t2m+1 , ∞) (88) then m (S ∪ N ) = [ k=1 t2k−1 (S ∪ N) − t2k (S ∪ N )] ∪ 2m+1 (S ∪ N) Other Þlter representations exist for different decompositions of instance, if the Þrst interval for begins at 0).

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Advances in Imaging and Electron Physics, Vol. 117 by Peter W. Hawkes

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