We describe a strategy for rigorous arbitrary-precision evaluation of Legendre polynomials on the unit interval and its application in the generation of Gauss-Legendre quadrature rules. Our focus is on making the evaluation practical for a wide range of realistic parameters, corresponding to the requirements of numerical integration to an accuracy of about 100 to 100 000 bits. Our algorithm com...

We consider the problem of recovering polynomials that are sparse with respect to the basis of Legendre polynomials from a small number of random samples. In particular, we show that a Legendre s-sparse polynomial of maximal degree N can be recovered fromm s log(N) random samples that are chosen independently according to the Chebyshev probability measure dν(x) = π−1(1 − x2)−1/2dx. As an effici...

In many applications, including analysis of seismic signals, Daubechies wavelets perform much better than other families wavelets. this paper, we provide a possible theoretical explanation for the empirical success Specifically, show that these are optimal with respect to any optimality criterion satisfies natural properties scale- and shift-invariance.

Pseudo Random Noise (PRN) codes are essential part in space communication. A pseudo random noise binary sequence is a semi-random sequence in the sense that it appears random within the sequence length, fulfilling the needs of randomness. The objective of the paper is to generate different types of PN sequences i.e. Legendre sequence, Weil sequence, Sidel’nikov sequence and polyphase Sidel’niko...

A new class of biorthogonal wavelets—interpolating distributed approximating functional (DAF) wavelets are proposed as a powerful basis for scale-space functional analysis and approximation. The important advantage is that these wavelets can be designed with infinite smoothness in both time and frequency spaces, and have as well symmetric interpolating characteristics. Boundary adaptive wavelet...

We devise a framework encompassing the classical theory of characteristics and the theory valid in the convex case recently obtained by R.T. Rockafellar and P. Wolenski. It relies on a notion of transform introduced by I. Ekeland. It involves a class of functions called Ekeland functions which is large enough to encompass convex functions, concave functions and linear-quadratic functions, as we...

Abstract: In this article we present problem recognizing gestures and signs executed by hands. Gesture recognition is the process by which gestures formed by a user interact with the computer or is the element of the special signs language to convey meaning.We propose a methods for the recognition of hand gestures using Gabor wavelets (GW ), Radon transform (RT ) and texture features for gestur...

Tensor product (separable) multivariate (bi)orthogonal wavelets have been widely used in many applications. On the other hand, non-tensor product (nonseparable) wavelets have been extensively argued in the literature to have many advantages over separable wavelets, for example, more freedom in design of nonseparable wavelets (such design is typically much more complicated and di±cult than the a...