Orthonormal polynomial wavelets on the interval
نویسندگان
چکیده
منابع مشابه
Orthonormal Polynomial Wavelets on the Interval
We use special functions and orthonormal wavelet bases on the real line to construct wavelet-like bases. With these wavelets we can construct polynomial bases on the interval; moreover, we can use them for the numerical resolution of degenerate elliptic operators.
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We construct an orthogonal wavelet basis for the interval using a linear combination of Legendre polynomials. The coefficients are taken as appropriate roots of Chebyshev polynomials of the second kind. The one-dimensional transform is applied to analytical data and appropriate definitions of a scalogram as well as local and global spectra are presented. The transform is then extended to the mu...
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In this paper we discuss closed form representations of filter coefficients of wavelets on the real line, half real line and on compact intervals. We show that computer algebra can be applied to achieve this task. Moreover, we present a matrix analytical approach that unifies constructions of wavelets on the interval.
متن کاملOn orthonormal wavelets and paraunitary filter banks
Binary tree-structured filter banks have been employed in the past to generate wavelet bases. While the relation between paraunitary filter banks and orthonormal bases is known to some extent, there are some extensions which are either not known, or not published so far. In particular it is known that a binary tree-structured filter bank with the same paraunitary polyphase matrix on all levels ...
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In this paper we generalize the constructions 5], 8] and 21] of wavelets on the interval. These schemes give boundary modiications of compactly supported orthogonal wavelets 2 L 2 (R) with supp = ?N + 1; N], where N denotes the number of vanishing moments of. Our new scheme overcomes this restrictive condition. Furthermore, the constructions 5], 8], 21] involve Gram matrices for explicit orthog...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2005
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-05-08088-3