Abstract A steady forced Korteweg–de Vries (fKdV) model which includes gravity, capillary, and pressure distributions is solved numerically using the wavelet Galerkin method. The anti-derivatives of Daubechies wavelets are developed as basis solution subspaces for mixed boundary condition type. Accuracy numerical solutions can be improved by increasing number levels in multi-resolution analysis...

Wavelet theory is an attempt to address the pervasive problem of describing the frequency content of a function locally in time. The wavelet approach is to analyze a function using an appropriate family of dilates and translates of one or more wavelets. Although this term is relatively new, wavelet-like techniques have been independently invented over the past 30 years in harmonic analysis, qua...

The Discrete Wavelet Transform (DWT) has extensively been used in a wide range of applications, including numerical analysis, image and video coding, pattern recognition, medical and telemetric imaging, etc. The invention of DWT decomposition by Mallat (Mallat, 1998) shows that the DWT can be viewed as a multiresolution decomposition of signal. This means it decomposes the signal into its compo...

In this paper, we first investigate the power spectral densities (PSD) of bipolar modulated Direct Sequence Ultra Wide Band (DS-UWB) signals using various pulse shapes under the FCC UWB emission mask. Considered pulse shapes are the first five derivatives of the Gauss pulse (p1, p2, p3, p4 and p5), the first four orthogonal modified Hermite waveforms, and Daubechies wavelets (db-q). It is obser...

A unifying algorithm has been developed to systematize the collection of compact Daubechies wavelets computable by spectral factorization of a symmetric positive polynomial. This collection comprises all classes of real and complex orthogonal and biorthogonal wavelet filters with maximal flatness for their minimal length. The main algorithm incorporates spectral factorization of the Daubechies ...

We consider wavelets as a tool to perform a variety of tasks in the context of analyzing cosmic microwave background (CMB) maps. Using Spherical Haar Wavelets we define a position and angular-scale-dependent measure of power that can be used to assess the existence of spatial structure. We apply planar Daubechies wavelets for the identification and removal of points sources from small sections ...

Since the publication, less than ten years ago, of Mallat's paper on Mul-tiresoltion Analysis Ma], and Daubechies' paper on the construction of smooth compactly supported wavelets D], wavelets had gained enormous popularity in mathematics and in the application domains. It is suucient to note that there are currently more than 10,000 subscribers to the monthly Wavelet Digest. At the same time, ...

Recently, research on two distinct types of wavelet frames have emerged, each with its own characteristics. The dual-tree discrete wavelet transform (DWT) [1] is based on the concatenation of two wavelet bases, where the two wavelets are designed to form a Hilbert transform pair, Ãg(t) = HfÃh(t)g [4]. A second type of wavelet frame is based on a single scaling function and two distinct wavelets...

Physical modelling of musical instruments is one possible approach to digital sound synthesis techniques. By the term physical modelling, we refer to the simulation of sound production mechanism of a musical instrument, which is modelled with reference to the physics using wave-guides. One of the fundamental parameters of such a physical model is the pitch, and so pitch period estimation is one...

Before medical images can be distributed online, it is necessary for con dentiality reasons to eliminate text that appears in the image. This paper describes TIDE (Textual Information Detection and Elimination) system for secure medical image distribution. The algorithm uses Daubechies' wavelets to detect and eliminate areas of textual information within digital medical images. The system is pr...