In this paper, we introduce a wavelet method for the description, approximation, analysis and simulation of optical surfaces. We describe the new method and show results of several numerical experiments for relevant applications in optics. We focus on three main aspects. First, we describe a highly accurate representation of smooth optical surfaces in terms of a B-spline quasi-interpolant. This...

In this paper, local cubic quasi-interpolating splines on non-uniform grids are described. The splines are computed by fast computational algorithms that utilize the relation between splines and cubic interpolation polynomials. These splines provide an efficient tool for real-time signal processing. As an input, they use either clean or noised arbitrarily-spaced samples. Exact estimations of th...

This paper proposes a novel method to detect fire and/or flames in real-time by processing the video data generated by an ordinary camera monitoring a scene. In addition to ordinary motion and color clues, flame and fire flicker is detected by analyzing the video in the wavelet domain. Quasi-periodic behavior in flame boundaries is detected by performing temporal wavelet transform. Color variat...

A novel optimized wavelet packet algorithm is proposed to improve the perception of sensorineural hearing-impaired people. In this work, we have developed optimized wavelet packet along with, biorthogonal wavelet basis functions using MATLAB Code. Here, we have created eight bands based on auditory filters of quasi octave bandwidth. Evaluation was carried out by conducting listening tests on se...

Wavelet transform has introduced a plethora of new aspects in signal and image processing over the last twenty years. It has significantly expanded the signal analyst’s capabilities and offers certain advantages over classical fourier transform (FFT) or shorttime fourier analysis (SFFT). The investigation of the suitability of the wavelet transform to handle Acoustic Emission signals has attrac...

This article is devoted to the study of wavelets based on the theory of shift-invariant spaces. It consists of two, essentially disjoint, parts. In the rst part, the berization of the analysis operator of a shift-invariant system is discussed. That berization applies to wavelet systems via the notion of quasi-wavelet systems, and leads to the theory of wavelet frames. Highlights in this theory ...

A wavelet-based method is re-introduced in an oceanographic and spectral context to estimate wavenumber spectrum flux of kinetic energy enstrophy. We apply this a numerical simulation idealized, doubly periodic quasi-geostrophic flows, that is, the flow constrained by Coriolis force vertical stratification. The double periodicity allows for straightforward Fourier analysis as baseline method. O...

We report the observation of non-stationary Quasi-Periodic Pulsations (QPPs) in high-energy particles during impulsive phase an X4.8 flare on 2002 July 23 (SOL2002-07-23T00:35). The was simultaneously measured by Reuven Ramaty High Energy Solar Spectroscopic Imager, Nobeyama Radio Polarimeters, and Radioheliograph. quasi-period about 50 s, determined wavelet transform, is detected Gamma-ray lin...

Our main concern in this paper is the design of simplified filtering procedures for the quasi-optimal approximation of functions in subspaces of L2 generated from the translates of a function φ(x). Examples of signal representations that fall into this framework are Schoenberg’s polynomial splines of degree n, and the various multiresolution spaces associated with the wavelet transform. After a...

Factorization of matrices Laurent polynomials plays an important role in mathematics and engineering such as wavelet frame construction filter bank design. Wavelet frames (a.k.a. framelets) are useful applications signal image processing. Motivated by the recent development quasi-tight framelets, we study characterize generalized spectral factorizations with symmetry for 2×2 polynomials. Applyi...