Asymptotic expansions of the wavelet transform for large and small values of the translation parameter b are obtained using asymptotic expansions of the Fourier transforms of the function and the wavelet. Asymptotic expansions of Mexican hat wavelet transform, Morlet wavelet transform, and Haar wavelet transform are obtained as special cases. Asymptotic expansion of the wavelet transform has al...

In this paper, a two-dimensional multi-wavelet is constructed in terms of Chebyshev polynomials. The constructed multi-wavelet is an orthonormal basis for space. By discretizing two-dimensional Fredholm integral equation reduce to a algebraic system. The obtained system is solved by the Galerkin method in the subspace of by using two-dimensional multi-wavelet bases. Because the bases of subs...

Besides many advantages of wavelet transform, it has several drawbacks, e.g. ringing, shift variance, aliasing and lack of directionality. Some of them can be eliminated by using wavelet packet transform, stationary wavelet transform, complex wavelet transform, adaptive directional lifting-based wavelet transform, or adaptive wavelet filter banks that use either L2 or L1 norm. This paper contai...

Let  $varpi$ be a representation of the homogeneous space $G/H$, where $G$ be a locally compact group and  $H$ be a compact subgroup of $G$. For  an admissible wavelet $zeta$ for $varpi$  and $psi in L^p(G/H), 1leq p <infty$, we determine a class of bounded  compact operators  which are related to continuous wavelet transforms on homogeneous spaces and they are called localization operators.

in this study, several data-driven techniques including system identification, adaptive neuro-fuzzy inference system (anfis), artificial neural network (ann) and wavelet-artificial neural network (wavelet-ann) models were applied to model rainfall-runoff (rr) relationship. for this purpose, the daily stream flow time series of hydrometric station of hajighoshan on gorgan river and the daily rai...

abstract most structural failures are because of break in consisting materials. these breaks are initiated with crack extension, which is a serious threat to the behavior of structure, so different methods have been developed for distinguishing and showing such cracks. meanwhile, the new methods based on original wavelet transform are efficient and very important in the subject of signals. the ...

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 ...

In this article, we propose a new method for selecting level dependent threshold in wavelet shrinkage using the empirical Bayes framework. We employ both Bayesian and frequentist testing hypothesis instead of point estimation method. The best test yields the best prior and hence the more appropriate wavelet thresholds. The standard model functions are used to illustrate the performance of the p...