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Minimum rate sampling and reconstruction of signals with arbitrary frequency support
 IEEE Trans. Inform. Theory
, 1999
"... Abstract—We examine the question of reconstruction of signals from periodic nonuniform samples. This involves discarding samples from a uniformly sampled signal in some periodic fashion. We give a characterization of the signals that can be reconstructed at exactly the minimum rate once a nonuniform ..."
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Abstract—We examine the question of reconstruction of signals from periodic nonuniform samples. This involves discarding samples from a uniformly sampled signal in some periodic fashion. We give a characterization of the signals that can be reconstructed at exactly the minimum rate once a nonuniform sampling pattern has been fixed. We give an implicit characterization of the reconstruction system, and a design method by which the ideal reconstruction filters may be approximated. We demonstrate that for certain spectral supports the minimum rate can be approached or achieved using reconstruction schemes of much lower complexity than those arrived at by using spectral slicing, as in earlier work. Previous work on multiband signals have typically been those for which restrictive assumptions on the sizes and positions of the bands have been made, or where the minimum rate was approached asymptotically. We show that the class of multiband signals which can be reconstructed exactly is shown to be far larger than previously considered. When approaching the minimum rate, this freedom allows us, in certain cases to have a far less complex reconstruction system. Index Terms — Multiband, nonuniform, reconstruction, sampling. I.
The systematized collection of Daubechies wavelets
 Tech. Rep. CT199806, Computational Toolsmiths
, 1998
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Sobolev Regularity For Rank M Wavelets
 CML Rep., Rice Univ
, 1997
"... . This paper explores the Sobolev regularity of rank M wavelets and refinement schemes. We find that the regularity of orthogonal wavelets with maximal vanishing moments grows at most logarithmically with filter length when M is odd, but linearly for even M . When M = 3 and M = 4, we show that the r ..."
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. This paper explores the Sobolev regularity of rank M wavelets and refinement schemes. We find that the regularity of orthogonal wavelets with maximal vanishing moments grows at most logarithmically with filter length when M is odd, but linearly for even M . When M = 3 and M = 4, we show that the regularity does achieve these upper bounds for asymptotic growth, complementing earlier results for M = 2. A new class of wavelet filters is introduced, by asserting zeros of the wavelet symbol at preperiodic points of the mapping ø : ! !M! mod 2ß. While this class includes the generalized Daubechies wavelets, numerical experiments demonstrate that the class also includes wavelet families with greater smoothness for a given filter length. Finally, members of the class of wavelets that have maximal Sobolev regularity for a given filter length are found as the solution to an optimization problem. Key words. wavelets, refinement equations, Sobolev regularity, smoothness, filter design AMS subj...
Optimal Design Of Multirate Systems
, 1995
"... ... approximation error over traditional design techniques is obtained. Finally, the design of cascade systems is considered. Optimal designs for these systems are found to provide additional reduction in computational complexity. ..."
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... approximation error over traditional design techniques is obtained. Finally, the design of cascade systems is considered. Optimal designs for these systems are found to provide additional reduction in computational complexity.