In the present study using the wavelet theory (WT) and later the nonlinear spectrum response of the acceleration (NSRA) resulted in estimating a strong earthquake record for the structure to a degree of freedom. WT was used in order to estimate the acceleration of earthquake mapping with equal sampling method (WTESM). Therefore, at first, the acceleration recorded in an earthquake using WTESM w...

In this paper we study the usage of wavelet in inverse problem multiplayer soil.We put forward a function and prove it is a wavelet function. Then we do theory analysis in detail about the application in computing soil parameters. At the same time, we do numerical experiments with two and three levels soil structure. The results indicate the valid of method

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.

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.

Wavelet decomposition and its related nonlinear approximation problem are investigated on the basis of shift invariant spaces of functions. In particular, a Bernstein type inequality associated with wavelet decomposition is established in such a general setting. Several examples of piecewise polynomial spaces are given to illustrate the general theory. AMS Subject Classifications: 41 A 17, 41 A...

The surface autocorrelation function can be retrieved from the values of the far-field integrated irradiance. The inversion procedure is discussed in the frame of a theory of integrated wavelet transformation. For different types of autocorrelation functions, the capabilities and limitations of the inversion procedure are studied. The influence of experimental noise and the specific choice of t...

Wavelet methods are widely used to decompose fMRI, EEG, or MEG signals into time series representing neurophysiological activity in fixed frequency bands. Using these time series, one can estimate frequency-band specific functional connectivity between sensors or regions of interest, and thereby construct functional brain networks that can be examined from a graph theoretic perspective. Despite...

In this paper, we study nonhomogeneous wavelet systems which have close relations to the fast wavelet transform and homogeneous wavelet systems. We introduce and characterize a pair of frequency-based nonhomogeneous dual wavelet frames in the distribution space; the proposed notion enables us to completely separate the perfect reconstruction property of a wavelet system from its stability prope...

We consider two types of Besov spaces on the Koch curve, defined by traces and with the help of the snowflaked transform. We compare these spaces and give their characterization in terms of Daubechies wavelets.

We introduce the theory of frames and develop wavelet theory as a natural extension of the Classical Sampling Theorem. This material serves as background for our applications to periodicity detection, noise reduction, and multidimensional irregular sampling.