Wavelet packet transform decomposes a signal into a set of orthonormal bases (nodes) and provides opportunities to select an appropriate set of these bases for feature extraction. In this paper, multi-level basis selection (MLBS) is proposed to preserve the most informative bases of a wavelet packet decomposition tree through removing less informative bases by applying three exclusion criteria:...

We describe a space and time adaptive numerical method based on wavelet orthonormal bases for solving partial diierential equations. The multiresolution structure of wavelet orthonormal bases provides a simple way to adapt computational reenements to the local regularity of the solution 11] 16]. High resolution computations are performed only in regions where singularities or sharp transitions ...

We study the limit distribution of zeros of certain sequences of holomorphic sections of high powers L of a positive holomorphic Hermitian line bundle L over a compact complex manifold M . Our first result concerns ‘random’ sequences of sections. Using the natural probability measure on the space of sequences of orthonormal bases {SN j } of H(M,L ), we show that for almost every sequence {SN j ...

Orthonormal M-band wavelet bases have been constructed and applied by several authors. This paper makes three main contributions. First, it generalizes the minimal length Kregular 2-band wavelets of Daubechies to the M-band case by deriving explicit formulas for K-regular M-band scaling filters. Several equivalent characterizations of K-regularity are given and their significance explained. Sec...

The investigation of flutter and aeroservoelastic stability through flight testing is an essential part of aircraft certification. The stability boundary prediction is especially difficult when the instability is associated with nonlinearity in the dynamics. This paper presents an approach for the characterization of the nonlinear dynamics by non-iterative identification algorithms. Two differe...

This paper investigates the mathematical framework of multiresolution analysis based on irregularly spaced knots sequence. Our presentation is based on the construction of nested nonuniform spline multiresolution spaces. From these spaces, we present the construction of orthonormal scaling and wavelet basis functions on bounded intervals. For any arbitrary degree of the spline function, we prov...

A novel method for learning optimal, orthonormal wavelet bases for representing 1and 2D signals, based on parallels between the wavelet transform and fully connected artificial neural networks, is described. The structural similarities between these two concepts are reviewed and combined to a “wavenet”, allowing for the direct learning of optimal wavelet filter coefficient through stochastic gr...

Numerical algorithms using wavelet bases are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in the new system of coordinates. As in all transform methods, such approach seeks an advantage in that the computation is faster in the new system of coordinates than in the original domain. However, due to the recursive definit...

This paper presents an algebraic approach to construct Mband orthogonal wavelet bases. A system of constraint equations is obtained for M-band orthonormal filters, and then a solution based on SVD (Singular Value Decomposition) is developed to enable us to produce innumerable wavelet bases of given length. Also the property of 2 vanishing moments is integrated into our wavelet construction proc...