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- J. A. Hogan, J. D. Lakey
- 1995

Two standard tools for signal analysis are the short{time Fourier transform and the continuous wavelet transform. These tools arise as matrix coeecients of square integrable representations of the Heisenberg and aane groups respectively, and discrete frame decompositions of L 2 arise from approximations of corresponding reproducing formulae. Here we study… (More)

- Scott Izu, Joseph D. Lakey
- 2008

This paper begins with a review of some classical work of Landau, Slepian, Pollak and Widom concerning essentially timeand bandlimited signals and ends reviewing some recent work of Candès, Romberg and Tao that places specific but probabilistic limitations on essential timeand bandlimiting for finite signals and their discrete Fourier transforms. In between… (More)

In this paper we construct a family of divergence-free multiwavelets. The construction follows Lemari e's procedure. In the process we nd multiresolution analyses (MRA) related by diierentiation and integration to a family of biorthogonal MRAs constructed by Hardin and Marasovich. The multiscaling and multiwavelets constructed have symmetries and support… (More)

This paper reviews several ideas that grew out of observations of Djokovic and Vaidyanathan to the effect that a generalized sampling method for bandlimited functions, due to Papoulis, could be carried over in many cases to the spline spaces and other shift-invariant spaces. Papoulis’ method is based on sampling output of linear, time-invariant systems.… (More)

- J. A. Hogan, Joseph D. Lakey
- IJWMIP
- 2005

In this paper we construct IR n-valued biorthogonal, compactly supported multiwavelet families such that one of the biorthogo-nal pairs consists of divergence-free vector wavelets. The construction is based largely on Lemari e's idea of multiresolution analyses intertwined by diierentiation. We show that this technique extends nontrivially to multiwavelets… (More)

- Joseph D. Lakey
- 2007

- J. D. Lakey
- 1998

We show that there are no biorthogonal pairs of divergence-free multi-wavelet families on R n , having any regularity, such that both biorthog-onal families have compactly supported, divergence-free generators. This main result generalizes Lemari e's bivariate result. In particular, our method is based on vector-valued multiresolution analyses.

- Jeffrey A. Hogan, Joseph D. Lakey
- 2015 International Conference on Sampling Theory…
- 2015

We refer to eigenfunctions of the kernel corresponding to truncation in a time interval followed by truncation in a frequency band as bandpass prelates (BPPs). We prove frame bounds for certain families of shifts of bandpass prolates, and we numerically construct dual frames for finite dimensional analogues. In the continuous case, the corresponding… (More)

- Joseph D. Lakey, Phan Nguyen
- Axioms
- 2013

We use the biorthogonal multiwavelets related by differentiation constructed in previous work to construct compactly supported biorthogonal multiwavelet bases for the space of vector fields on the upper half plane R+ such that the reconstruction wavelets are divergence-free and have vanishing normal components on the boundary of R+. Such wavelets are… (More)