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- Title
From Filters to Wavelets via Direct Limits II: Wavelet-Packet Bases.
- Authors
Raeburn, IIain
- Abstract
In recent joint work with Nadia Larsen, we gave a new proof of a theorem of Mallat which describes how to construct wavelets from quadrature mirror filters. Our main innovation was to show how the scaling function associated to the filter can be used to identify a particular direct limit of Hilbert spaces with L2(ℝ). Here we show that wavelet-packet bases for L2(ℝ) also fit naturally into the same direct-limit framework.
- Subjects
WAVELETS (Mathematics); HILBERT space; LARSEN, Nadia; PROOF theory; ISOMORPHISM (Mathematics); FOURIER transforms; NATURAL numbers
- Publication
Acta Applicandae Mathematicae, 2009, Vol 108, Issue 3, p509
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-008-9425-x