Construction of Parseval wavelets from redundant filter systems
نویسندگان
چکیده
منابع مشابه
Orthonormal Dilations of Parseval Wavelets
We prove that any Parseval wavelet frame is the projection of an orthonormal wavelet basis for a representation of the Baumslag-Solitar group BS(1, 2) = 〈u, t | utu = t〉. We give a precise description of this representation in some special cases, and show that for wavelet sets, it is related to symbolic dynamics (Theorem 3.14). We show that the structure of the representation depends on the ana...
متن کاملLinear Independence of Parseval Wavelets
We establish several results yielding linear independence of the affine system generated by ψ in exchange for conditions on the space V (ψ) of negative dilates. A typical assumption yielding linear independence is that the space V (ψ) is shift-invariant. In particular, the affine system generated by a Parseval wavelet is linearly independent. As an illustration of our techniques, we give an alt...
متن کاملFurther Results on the Connectivity of Parseval Frame Wavelets
New ideas were introduced in [3] to treat the problem of connectivity of Parseval frames. With these ideas it was shown that a large set of Parseval frames is arcwise connected. In this article we exhibit a larger class of Parseval frames for which the arcwise connectivity is true. This larger class fails to include all Parseval frames.
متن کاملMinimally Supported Frequency Composite Dilation Parseval Frame Wavelets
Abstract. A composite dilation Parseval frame wavelet is a collection of functions generating a Parseval frame for L2(Rn) under the actions of translations from a full rank lattice and dilations by products of elements of groups A and B. A minimally supported frequency composite dilation Parseval frame wavelet has generating functions whose Fourier transforms are characteristic functions of set...
متن کاملConstruction of biorthogonal wavelets from pseudo-splines
Pseudo-splines constitute a new class of refinable functions with B-splines, interpolatory refinable functions and refinable functions with orthonormal shifts as special examples. Pseudo-splines were first introduced by Daubechies, Han, Ron and Shen in [Framelets: MRA-based constructions of wavelet frames, Appl. Comput. Harmon. Anal. 14(1) (2003), 1–46] and Selenick in [Smooth wavelet tight fra...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2005
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.1982768