Reprinted with Permission of Kluwer Academic Publishers Some Stability Properties of Wavelets and Scaling Functionsy
نویسنده
چکیده
The property of continuity of an arbitrary scaling function is known to be unstable with respect to the coeecients in the associated dilation equation. That is, if f is a continuous function which is a solution of the dilation equation f (x) = P N k=0 c k f (2x ? k) then a dilation equation with slightly perturbed coeecients f~ c 0 ; : : : ; ~ c N g need not have a continuous solution. The convergence of the Cascade Algorithm, an iterative method for solving a dilation equation, is likewise unstable in general. This paper establishes a condition under which stability does occur: both continuity and uniform convergence of the Cascade Algorithm are shown to be stable for those initial choices of coeecients fc 0 ; : : : ; c N g such that the integer translates of the scaling function f arè 1 linearly independent. In particular, this applies to those scaling functions which can be used to construct orthogonal or biorthogonal wavelets. We show by example that this`1 linear independence condition is not necessary for stability to occur.
منابع مشابه
Kant , Kuhn , and the Rationality of Science
†Send requests for reprints to the author, Department of History and Philosophy of Science, Goodbody Hall 130, Indiana University, 1011 East Third Street, Bloomington, IN 47405–7005; e-mail: [email protected]. *This paper first appeared in Michael Heidelberger and Friedrich Stadler (eds.) History of Philosophy of Science: New Trends and Perspectives (Dordrecht: Kluwer, 2002) Kluwer Academic ...
متن کاملReprinted with permission of KLUWER ACADEMIC/PLENUM PUBLISHERS To be published in Ultra-Wideband, Short-Pulse Electromagnetics RECENT APPLICATIONS OF ULTRA WIDEBAND RADAR AND COMMUNICATIONS SYSTEMS
After a very short introduction to the history and theory of ultra wideband technology, we describe the current state-of-the-art (within the United States) in this emerging field by way of examples of recently fielded UWB hardware and equipment. Multispectral Solutions, Inc. (MSSI) is a pioneer and an established industry leader in the development of ultra wideband systems and has been actively...
متن کاملVarieties of Unital `-Groups and ΨMV-Algebras
(Day 1): References (for general background) →Varieties of lattice-ordered groups, N. R. Reilly, in Lattice-Ordered Groups, Advances and Techniques, A. M. W. Glass and W. C. Holland (eds.), Kluwer Academic Publishers, 1989. Lattice-Ordered Groups, an Introduction, M. Anderson and T. Feil, D. Reidel Pub. Co., 1988. Theory of Lattice-Ordered Groups, M. Darnel, Marcel Dekker, 1995. Partially Order...
متن کاملSolving optimal control problems with integral equations or integral equations - differential with the help of cubic B-spline scaling functions and wavelets
In this paper, a numerical method based on cubic B-spline scaling functions and wavelets for solving optimal control problems with the dynamical system of the integral equation or the differential-integral equation is discussed. The Operational matrices of derivative and integration of the product of two cubic B-spline wavelet vectors, collocation method and Gauss-Legendre integration rule for ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1994