A novel and effective method based on Haar wavelets and Block Pulse Functions (BPFs) is proposed to solve nonlinear Fredholm integro-differential equations of fractional order. The operational matrix of Haar wavelets via BPFs is derived and together with Haar wavelet operational matrix of fractional integration are used to transform the mentioned equation to a system of algebraic equations. Our...

We present a novel method of classification and segmentation of melodies in symbolic representation. The method is based on filtering pitch as a signal over time with the Haar-wavelet, and we evaluate it on two tasks. The filtered signal corresponds to a single-scale signal ws from the continuous Haar wavelet transform. The melodies are first segmented using local maxima or zero-crossings of ws...

We present here, simple iterative technique for solving some models of nonlinear partial differential equations using Haar wavelet. Numerical examples are given to establish the efficiency and accuracy of the present method.

Application of the Haar wavelet approach for solving stiff differential equations is discussed. Solution of singular perturbation problems is also considered. Efficiency of the recommended method is demonstrated by means of four numerical examples, mostly taken from well-known textbooks.

We develop a tool to approximate the entries of a large dimensional complex Jacobi ensemble with independent complex Gaussian random variables. Based on this and the author’s earlier work in this direction, we obtain the Tracy-Widom law of the largest singular values of the Jacobi emsemble. Moreover, the circular law, the Marchenko-Pastur law, the central limit theorem, and the laws of large nu...

In this paper, we present the multilevel adaptive wavelet collocation method for solving non-divergent barotropic vorticity equation over spherical geodesic grid. This method is based on multi-dimensional second generation wavelet over a spherical geodesic grid. The method is more useful in capturing, identifying, and analyzing local structure [1] than any other traditional methods (i.e. finite...

In this paper a watermarking method based on the Haar wavelet transform is proposed. The hiding procedure is performed in the LL subband of the first level of Haar decomposition of the image. The coefficients resilient to specific attacks are modified in order to obtain a robust embedding scheme. The proposed method is used to define a mask to perform the embedding in the wavelet transform doma...

Many global illumination algorithms generate directionally-and positionally-varying radiance data that then need to be somehow re-sampled and used for nal shading. This operation should lter all light over the incident hemisphere through the BRDF to generate an accurate image. This can be done analytically for simple BRDFs, such as Lambertian or Phong-like BRDFs, but becomes more diicult in the...

The multiresolution time-domain (MRTD) algorithm is applied to the problem of general two-dimensional electromagnetic scattering. A Haar wavelet expansion is utilized. A parallel between Haar MRTD and the classic Yee finite difference time-domain (FDTD) algorithm is discussed, and results of simulations on canonical targets are shown for comparison. We focus on the incident-field implementation...

In this paper, we proposed a new method to develop secure image-encryption techniques using a logistics -based encryption algorithm. In this technique, a Haar wavelet transform was used to decompose the image and decorrelate its pixels into averaging and differencing components. The logistic based encryption algorithm produces a cipher of the test image that has good diffusion and confusion pro...