This paper aims to study the q-wavelet and the q-wavelet transforms, associated with the q-Bessel operator for a fixed q ∈]0, 1[. As an application, an inversion formulas of the q-Riemann-Liouville and q-Weyl transforms using qwavelets are given. For this purpose, we shall attempt to extend the classical theory by giving their q-analogues.

This paper aims to study the q-wavelet and the q-wavelet transforms, associated with the q-Bessel operator for a fix q ∈]0, 1[. As application, an inversion formulas of the q-Riemann-Liouville and q-Weyl transforms using q-wavelets are given. For this purpose, we shall attempt to extend the classical theory by giving their q-analogues.

One of the major driven forces in the area of applied and computational harmonic analysis over the last decade or longer is the development of redundant systems that have sparse approximations of various classes of functions. Such redundant systems include framelet (tight wavelet frame), ridgelet, curvelet, shearlet and so on. This paper mainly focuses on a special class of such redundant syste...

The paper is devoted to theoretical and computational studies on application of the multiresolutional wavelet-based homogenization approach in the Finite Element Method modeling of heterogeneous media. Multiresolutional homogenization scheme is proposed for 1D elastostatic equilibrium problem of periodic heterogeneous medium with Young modulus defined by some elementary wavelet functions and co...

In this letter, the wavelet transform is used to decompose classical linearly polarized plane light wave into a series of discrete Morlet wavelets. It found that energy can be discrete, associated with its structure.It also changeable basic packet or train vector $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}}\over k} $ and structure form ${H_{0k}} = n{p_{0k}}\omega$ $(...

Classical nondecimated wavelet transforms are attractive for many applications. When the data comes from complex or irregular designs, the use of second generation wavelets in nonparametric regression has proved superior to that of classical wavelets. However, the construction of a nondecimated second generation wavelet transform is not obvious. In this paper we propose a new ‘nondecimated’ lif...

In this paper we deal with local Besov spaces of periodic functions of one variable. We characterize these spaces in terms of summability conditions on the coefficients in series expansions of their elements with respect to an orthogonal Schauder basis of trigonometric polynomials. We consider a Schauder basis that was constructed by using ideas of a periodic multiresolution analysis and corres...

We consider the problem of constructing indices to image and video data analogous to those used in classical database systems, in order to speed up the retrieval of such data from physical storage (either local or remote). To achieve this goal, we propose new coding techniques which combine a wavelet representation, embedded coding of the wavelet coe cients, and segmentation of image-domain reg...

The orthogonal frequency division multiplexing is used in wireless communication due to high data rate. OFDM are robustness against multi-path fading, frequency selective fading, and narrow band interference. Wavelet analysis has strong advantages over fourier transform and also allows time-frequency domain operation with flexibility. Wavelet is applied in various fields of wireless communicati...

finite affine groups are given by groups of translations and di-lations on finite cyclic groups. for cyclic groups of prime orderwe develop a time-scale (wavelet) analysis and show that for alarge class of non-zero window signals/vectors, the generatedfull cyclic wavelet system constitutes a frame whose canonicaldual is a cyclic wavelet frame.