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Constructing pairs of dual bandlimited frame wavelets in $L^2(\mathbb{R}^n)$ (1009.4351v1)

Published 22 Sep 2010 in math.FA

Abstract: Given a real, expansive dilation matrix we prove that any bandlimited function $\psi \in L2(\mathbb{R}n)$, for which the dilations of its Fourier transform form a partition of unity, generates a wavelet frame for certain translation lattices. Moreover, there exists a dual wavelet frame generated by a finite linear combination of dilations of $\psi$ with explicitly given coefficients. The result allows a simple construction procedure for pairs of dual wavelet frames whose generators have compact support in the Fourier domain and desired time localization. The construction relies on a technical condition on $\psi$, and we exhibit a general class of function satisfying this condition.

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