Scaling equations are used to derive formulae of quadratures involving polynomials and scaling/wavelet functions with compact supports; in particular, those discovered by Daubechies. It turns out that with a few parameters, which are theoretically exact, these quadratures can be evaluated with algebraic formulae instead of numerical approximations. Those parameters can be obtained with high pre...

This study focuses on identifying damage in reinforced concrete (RC) beams using time-domain modal testing and wavelet analysis. A numerical model of an RC beam was used to generate various scenarios with different severities locations. Acceleration time histories were recorded for both damaged undamaged structures. Two indices, DI_MW DI_SW, derived from the analysis, employed determine locatio...

this paper concentrates on a new procedure which experimentally recognises gears and bearings faults of a typical gearbox system using a least square support vector machine (lssvm). two wavelet selection criteria maximum energy to shannon entropy ratio and maximum relative wavelet energy are used and compared to select an appropriate wavelet for feature extraction. the fault diagnosis method co...

this paper concentrates on a new procedure which experimentally recognises gears and bearings faults of a typical gearbox system using a least square support vector machine (lssvm). two wavelet selection criteria maximum energy to shannon entropy ratio and maximum relative wavelet energy are used and compared to select an appropriate wavelet for feature extraction. the fault diagnosis method co...

In recent years Image and Signal compression have been receiving a lot of attention by scientists and researchers in order to improve storage and transmission capabilities. In this study we have compared the performance of Kekre’s wavelet with other wavelets viz. Haar and Daubechies 2 with respect to energy in the Low-Low (LL ), Low-High (LH) ,High-Low (HL) and High-High (HH) bands. The energy ...

Explicit solutions are given for the rational function P (z) for two classes of IIR orthogonal 2-band wavelet bases, for which the scaling lter is maximally at. P (z) denotes the rational transfer function H(z)H(1=z) where H(z) is the (lowpass) scaling lter. The rst is the class of solutions that are intermediate , between the Daubechies and the Butterworth wavelets. It is found that the Daubec...

The LeGall 5/3 and Daubechies 9/7 filters have risen to special prominence because they were selected for inclusion in the JPEG2000 standard. We determine their key mathematical features: Riesz bounds, order of approximation, and regularity (Hölder and Sobolev). We give approximation theoretic quantities such as the asymptotic constant for the L2 error and the angle between the analysis and syn...

Abstract In this paper, we obtain some special types of integrals of Daubechies Wavelets which are used as Galerkin basis functions for numerical solution of partial differential equations of one dimension. Galerkin bases are constructed by integrating Daubechies functions which are compactly supported and which constitute an orthonormal basis of L2(R). Theoretical and numerical results are obt...

Computational algorithms have been developed for generating min-length max-flat FIR filter coefficients for orthogonal and biorthogonal wavelets with varying degrees of asymmetry or symmetry. These algorithms are based on spectral factorization of the Daubechies polynomial with a combinatorial search of root sets selected by a desired optimization criterion. Daubechies filter families were syst...