Abstract
A description of the fine structure of a refinable, shift-invariant sub-space of L 2(ℝ) is presented. This fine structure is exhibited through the existence of a canonical frame of functions in such a space, and a related notion of frequency content in these frame elements uniquely determines a multiplicity function that quantifies a redundancy of the frequencies. The refinability of the subspace can then be described by a pair of matrices of periodic functions that satisfy a set of equations, related to the multiplicity function, which play the role of high-dimensional filter equations.
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© 2006 Birkhäuser Boston
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Baggett, L. (2006). Redundancy in the Frequency Domain. In: Heil, C. (eds) Harmonic Analysis and Applications. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4504-7_15
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DOI: https://doi.org/10.1007/0-8176-4504-7_15
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-3778-1
Online ISBN: 978-0-8176-4504-5
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