Showing papers in "Applied and Computational Harmonic Analysis in 1993"

TL;DR: In this paper, the authors discuss several constructions of orthonormal wavelet bases on the interval, and introduce a new construction that avoids some of the disadvantages of earlier constructions.

TL;DR: Mallat′s Heuristic is formalized and proved, which says that wavelet bases are optimal for representing functions containing singularities, when there may be an arbitrary number of singularity distributed.

TL;DR: A non-parametric wavelet packet feature extraction procedure which identifies features to be used for the classification of transient signals for which explicit signal models are not available or appropriate and the promise of the method is illustrated by performing the procedure on a set of biologically generated underwater acoustic signals.

TL;DR: In this paper, the authors formulate several criteria on square-integrable functions in terms of certain smoothness and rate of decay that guarantee that these functions generate Bessel sequences, and show that one can obtain affine frames by arbitrarily oversampling any of the well-known wavelets.

TL;DR: In this paper, the exact frame coefficients are obtained in the natural limit if and only if a concrete condition is satisfied, where the condition is defined by a finite subsets of the frame.

TL;DR: In this paper, a time-scale representation of (acoustic) signals, motivated by the structure of the mammalian auditory system, is presented, and a theoretical framework is developed in which an iterative algorithm for reconstruction is constructed.

TL;DR: In this article, the relative error covariance matrix (RECM) is introduced as a tool for quantitatively evaluating the manner in which data contribute to the structure of a reconstruction.

TL;DR: In this paper, it was shown that certain oscillatory boundary integral operators occurring in acoustic scattering computations become sparse when represented in the appropriate local cosine transform orthonormal basis.

TL;DR: In this article, the authors describe an algorithm for the evaluation of Bessel functions J ν ( x ), Y ν( x ) and H ( j ) ν, x 1/3 for arbitrary positive orders and arguments at a constant CPU time.