Characterizations of tight over-sampled affine frame systems and over-sampling rates
Abbreviated Journal Title
Appl. Comput. Harmon. Anal.
MAXIMUM VANISHING MOMENTS; COMPACTLY SUPPORTED TIGHT; WAVELET FRAMES; R-N; DILATIONS; L-2(R-D); Mathematics, Applied; Physics, Mathematical
Let M be a dilation matrix, Psi a finite family of L-2-functions, and P the collection of all nonsingular matrices P such that M, P, and PMP-1 have integer entries. The objective of this paper is two-fold. First, for each P in P, we characterize all tight affine frames X (Psi, M) generated by Psi such that the over-sampled affine systems X (P) (Psi, M) relative to the "over-sampling rate" P remain to be tight frames. Second, we characterize all over-sampling rates P is an element of P, such that the over-sampled affine systems X (P) (Psi, M) are fight frames whenever the affine system X (Psi, M) is a tight frame. Our second result therefore provides a general and precise formulation of the second over-sampling theorem for tight affine frames. (C) 2006 Elsevier Inc. All rights reserved.
Applied and Computational Harmonic Analysis
"Characterizations of tight over-sampled affine frame systems and over-sampling rates" (2007). Faculty Bibliography 2000s. 6960.