International Journal of Wavelets, Multiresolution and Information Processing

The main objective of the proposed analysis is the detection of inter-turn short circuits in the stator windings of an induction machine. The analysis of the space vector current modulus of an induction motor is presented in this paper. This analysis is based on Daubechies 8 wavelet with seven decomposition levels. The 5th decomposition-level detail signal for a 4 kHz sampling frequency is chosen as a fault indicator, based on simulation results that show different behaviors of the energy contained in the detail signals independent of the percentage of load and fault levels. Experimental results that validate the proposed strategy are also presented. These results also show that the strategy is in addition immune to load variations as well as to feeding voltage unbalances.

In this article, we obtain two classes of non-MSF wavelets by considering two different classes of six-interval wavelet sets provided by Arcozzi, Behera and Madan (J. Geom. Anal.13 (2003) 557–579). Out of these classes one is countable, the non-MSF wavelets of which are non-MRA and the other one is uncountable, the non-MSF wavelets of which are MRA. The set of all non-MSF MRA wavelets of the latter class is shown to be pathconnected.

Based on a detailed analysis for the one-dimensional intrinsic mode function, a model of the bidimensional intrinsic mode function is found firstly. Then a new bidimensional empirical mode decomposition algorithm is developed by using the Radon transform. The existing methods have to locate the maxima and minima in a bidimensional function, and further, produce bidimensional envelopes. Those are usually hard for a real two-dimensional function. The proposed algorithm successfully avoids these difficulties. Experiments show encouraging results.

Currently, two-dimensional dyadic wavelet transform (2D-DWT) is habitually considered as the one presented by Mallat, which is defined by an approximation component, two detail components in horizontal and vertical directions. This paper is to introduce a new type of two-dimensional dyadic wavelet transform and its application so that dyadic wavelet can be studied and used widely furthermore. (1) Two-dimensional stationary dyadic wavelet transform (2D-SDWT) is proposed, it is defined by approximation coefficients, detail coefficients in horizontal, vertical and diagonal directions, which is essentially the extension of two-dimensional stationary wavelet transform for orthogonal/biorthogonal wavelet filters. (2) ε-decimated dyadic discrete wavelet transform (DDWT) is introduced and its relation with 2D-SDWT is given, where ε is a sequence of 0's and 1's. (3) Mallat decomposition algorithm based on dyadic wavelet is introduced as a special case of ε-decimated DDWT, and so a face recognition algorithm based on dyadic wavelet is proposed, and experimental results are given to show its effectiveness.

This paper is an investigation of shift invariant subspaces of L²(G), where G is a locally compact abelian group, or in general a local field, with a compact open subgroup. In this paper we state necessary and sufficient conditions for shifts of an element of L²(G) to be an orthonormal system or a Parseval frame. Also we show that each shift invariant subspace of L²(G) is a direct sum of principle shift invariant subspaces of L²(G) generated by Parseval frame generators.

We developed a new numerical procedure based on the quadratic semi-orthogonal B-spline scaling functions for solving a class of nonlinear integral equations of the Hammerstein-type. Properties of the B-spline wavelet method are utilized to reduce the Hammerstein equations to some algebraic equations. The advantage of our method is that the dimension of the arising algebraic equation is 10 × 10. The operational matrix of semi-orthogonal B-spline scaling functions is sparse which is easily applicable. Error estimation of the presented method is analyzed and proved. To demonstrate the validity and applicability of the technique the method applied to some illustrative examples and the maximum absolute error in the solutions are compared with the results in existing methods.^20,25,27,29

Following the oscillating theory of Meyer, many image decomposition models have been proposed to split an image into two parts: structures and textures. But these models are not effective in the case of a noisy image, because both textures and noise are oscillating patterns. In this paper, we use the local variance measure to separate noise from textures. Firstly, we examine the relationship between dyadic BMO norm and local variance. Then, we give the wavelet representation of dyadic BMO norm and local variance, and further propose a method to distinguish between texture and noise in wavelet domain. In high frequency wavelet domain, we propose a decomposition model using local variance as constraints, while in low frequency domain, we use the shrinkage scheme to distinguish them. Finally, we present various numerical results on images to demonstrate the potential of our method.

In this paper, we derive an algorithm to solve the linear quadratic (LQ) optimal regulator problems. The new approach is based on efficient Legendre and Chebyshev formulae at the Chebyshev–Gauss–Lobatto points. The technique enjoys advantages of both the Legendre and Chebyshev approximations near the end points. To show the numerical behavior of the proposed method, the simulation results of an example are presented.

In this paper, we describe an algorithm for computing biorthogonal compactly supported dyadic wavelets related to the Walsh functions on the positive half-line ℝ₊. It is noted that a similar technique can be applied in very general situations, e.g., in the case of Cantor and Vilenkin groups. Using the feedback-based approach, some numerical experiments comparing orthogonal and biorthogonal dyadic wavelets with the Haar, Daubechies, and biorthogonal 9/7 wavelets are prepared.

This paper deals with the construction of spline wavelets on the interval [0, 1], which have zero boundary values and vanishing moments. One begins with some primal scaling functions and their biorthogonal duals. Then desired biorthogonal wavelets are given by the method of Dahmen, Kunoth and Urban. Since the structure of those wavelets looks complicated, one tries to construct those types of wavelets only in primal side finally, without using any dual informations. Some numerical experiments show good effects, although the uniform stability remains to be proved theoretically.