By P. P. Vaidyanathan
featuring basic rules with no bias in the direction of particular application-oriented element, this article bargains a radical, unified, and in-depth therapy of the options of multirate sign processing. it's the first publication to hide the themes of electronic filter out banks, multidimensional multirate structures, and wavelet representations lower than one hide. This guide might be priceless to engineers operating with purposes of speech and picture compression, electronic audio, and statistical and adaptive sign processing.
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Additional info for Multirate Systems And Filter Banks
Design of optimal camera apertures adapted to display devices over arbitrary sampling lattices. IEEE Signal Process. , 11:443–445, 2004.  E. Dubois. Motion-compensated ﬁltering of time-varying images. Multidimensional Syst. , 3:211–239, 1992.  B. Girod and R. Thoma. Motion-compensating ﬁeld interpolation from interlaced and noninterlaced grids. In Proc. SPIE Image Coding, 594:186–193, 1985.  E. Dubois and J. Konrad. Estimation of 2-D motion ﬁelds from image sequences with application to motion-compensated processing.
24) where ٌ ϭ (Ѩ/Ѩx, Ѩ/Ѩy)T denotes the spatial gradient and ϭ (1 , 2 )T is the velocity to be estimated. The above constraint equation has served as the basis for many motion estimation algorithms. However, note that applied at single position (x, y) Eq. 24) is underconstrained (one equation, two unknowns) and allows to determine only the component of in the direction of image gradient ٌI . Thus, additional constraints are needed in order to uniquely solve for . Moreover, Eq. 24) does not hold exactly for real images, and usually a minimization of some function of (ٌI )T ϩ ѨI Ѩt is required.
Naturally, one would like to design a decision rule so that on average the cost associated with making a decision based on y is minimal. By computing an average risk, and by assuming that costs associated with erroneous decisions are higher than those associated with the corresponding correct decisions, it can be shown that an optimal decision can be made according to the following rule [1, Chapter 2]: P(Y ϭ y|H1 ) H1 0 ≷ . 1) The quantity on the left is called the likelihood ratio and is a constant dependent on the costs of the four scenarios.