In this study, we analyze the performance of a numerical scheme based on 3-scale Haar wavelets for dynamic Euler-Bernoulli equation, which is fourth order time dependent partial differential equation. This type equations governs behaviour vibrating beam and have many applications in elasticity. For its solution, first rewrite equation as system by introducing new variable, then use finite diffe...

A system is differentially flat if it is Lie–Bäcklund (L-B) equivalent to a free dynamical system that has dimensions equal to that of the input of the original system. Utilizing this equivalence, the problem of nonlinear model predictive control of a flat system can be reduced to a lower dimensional nonlinear programming problem with respect to the flat outputs. In this work, a novel computati...

Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation a non-linear, two parameter algebra. This structure can be mapped onto the quantum group suq(2) in one limit, and approaches a Fourier series generating alge...

Several studies have demonstrated the effectiveness of Haar wavelets in reducing large amounts of data down to compact wavelet synopses that can be used to obtain fast, accurate approximate query answers. While Haar wavelets were originally designed for minimizing the overall root-mean-squared (i.e., L2-norm) error in the data approximation, the recently-proposed idea of probabilistic wavelet s...

Wavelets are explored as a data smoothing (or de-noising) option for solution monitoring data in nuclear safeguards. In wavelet-smoothed data, the Gibbs phenomenon can obscure important data features that may be of interest. This paper compares wavelet smoothing to piecewise linear smoothing and local kernel smoothing, and illustrates that the Haar wavelet basis is effective for reducing the Gi...

In this paper, we present a computational method for solving stochastic VolteraFredholm integral equations which is based on the Haar wavelets and their stochastic operational matrix. Convergence and error analysis of the proposed method are worked out. Numerical results are compared with the block pulse functions method for some non-trivial examples. The obtained results reveal efficiency and ...

1 Facultatea de Electronică şi Telecomunicaţii, Departamentul Comunicaţii Bd. V. Pârvan Nr. 2, 300223 Timişoara, e-mail [email protected] Abstract – This paper presents an in-depth investigation of DWTbased OFDM, by analyzing the influence of the wavelets mother choice on the BER performance for the transmission in a flat fading channel. Simulations made show the importance of this param...

This work shows the use of a two-dimensional Gabor wavelets in image processing. Convolution with such a two-dimensional wavelet can be separated into two series of one-dimensional ones. The key idea of this work is to utilize a Gabor wavelet as a multiscale partial differential operator of a given order. Gabor wavelets are used here to detect edges, corners and blobs. A performance of such an ...

Regression or function classes of Euclidean type with compact support and certain smoothness properties are shown to be PAC learnable by the Nadaraya-Watson estimator based on complete orthonormal systems. While requiring more smoothness properties than typical PAC formulations, this estimator is computationally efficient, easy to implement, and known to perform well in a number of practical ap...

This paper reviews Ranklets, a family of multiscale, orientation-selective , non-parametric features modeled on Haar wavelets. Ranklets are related to wavelets and rank statistics. At the inception, a basic discussion on Ranklets is presented here. Next a focus is given to the various algorithms used so far to compute Ranklets with their complexities. The different applications of Ranklets in t...