Recent wavelet research has primarily focused on real-valued wavelet bases. However, complex wavelet bases ooer a number of potential advantageous properties. For example, it has been recently suggested 1], 2] that the complex Daubechies wavelet can be made symmetric. However, these papers always imply that if the complex basis has a symmetry property then it must exhibit linear phase as well. ...

The formalism of the one-dimensional discrete wavelet transform (DWT) based on Daubechies wavelet filters is outlined in terms of finite vectors and matrices. Both the scale-dependent wavelet variance and wavelet covariance are considered and confidence intervals for each are determined. The variance estimates are more accurately determined with a maximal-overlap version of the wavelet transfor...

Entropy as a measure of uncertainty was used to represent the results of the wavelet technique in electrochemical noise analysis. The experimental signals were obtained by recording the electrochemical potential and current noise of 7075 aluminum alloy in 3.5% NaCl solution. The electrochemical potential and current noise were decomposed into 16 levels using Daubechies wavelets. Wavelet output ...

We study embeddings between generalised Besov–Morrey spaces Nφ,p,qs(Rd). Both sufficient and necessary conditions for the are proved. Embeddings of into Lebesgue Lr(Rd) also considered. Our approach requires a wavelet characterisation which we establish system Daubechies wavelets.

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...

Analyses based on Symmetric Daubechies Wavelets (SDW) lead to complex-valued multiresolution representations of real signals. After a recall of the construction of the SDW, we present some speciic properties of these new types of Daubechies wavelets. We then discuss two applications in image processing: enhancement and restoration. In both cases, the eeciency of this multiscale representation r...

Image compression is process to remove the redundant information from the image so that only essential information are stored the storage size, transmission bandwidth and transmission time. In this paper comparative analysis of gray scale image compression is done by three different methods that are Daubechies Transform, Haar Transform and Biorthogonal Transform. Experimental results demonstrat...

In wavelet representations, the magnitude of the wavelet coeecients depends on both the smoothness of the represented function f and on the wavelet. We investigate the extreme values of wavelet coeecients for the standard function spaces A k = ff j kf (k) k 2 1g, k 2 N. In particular, we compare two important families of wavelets in this respect, the orthonormal Daubechies wavelets and the semi...