Preprint article · Journal article
Constructing pairs of dual bandlimited frame wavelets in L^2(R^n)
Given a real, expansive dilation matrix we prove that any bandlimited function ψ∈L2(Rn), 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 ψ 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 ψ, and we exhibit a general class of function satisfying this condition.
Language: | English |
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Year: | 2012 |
Pages: | 313-328 |
ISSN: | 1096603x and 10635203 |
Types: | Preprint article and Journal article |
DOI: | 10.1016/j.acha.2011.07.002 |
ORCIDs: | Lemvig, Jakob |