This chapter takes up the design of discrete wavelet transforms based on oversampled filter banks. In this case the wavelets form an overcomplete basis, or frame. In particular, we consider the design of systems that are analogous to Daubechies’ orthonormal wavelets — that is, the design of minimal length wavelet filters satisfying certain polynomial properties, but now in the oversampled case....

1 Système à représenter 3 1.1 Description générale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Les processus associés à la station graphique . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Processus associé au cas d’utilisation “Cas 1” : . . . . . . . . . . . . . . 4 1.2.2 Processus associé au cas d’utilisation “Cas 2” : . . . . . . . . . . . . . . 4 1.3 Les processus ...

Drought forecasting is essential for risk management and preparedness of drought mitigation measures. The present study aims to evaluate the effectiveness proposed hybrid technique regional forecasting. Multiple Linear Regression (MLR), Artificial Neural Network (ANN), two wavelet techniques, namely, Discrete Wavelet Transform (DWT) Packet (WPT), were evaluated in up a lead time six months. Sta...

‎In this paper‎, ‎Haar wavelets are performed for solving continuous time-variant linear-quadratic optimal control problems‎. ‎Firstly‎, ‎using necessary conditions for optimality‎, ‎the problem is changed into a two-boundary value problem (TBVP)‎. ‎Next‎, ‎Haar wavelets are applied for converting the TBVP‎, ‎as a system of differential equations‎, ‎in to a system of matrix algebraic equations‎...

This paper first shows that the Cohen-Daubechies-Feauveau (C-D-F) biorthogonal wavelet can be derived from the interpolating wavelet through a lifting process. Its high-pass filter measures the interpolation error of the averaged data. Next, we propose a new wavelet method, called the difference wavelet method, for efficient representation for functions on R. Its analysis part is simply averagi...

It is well known that the Haar and Shannon wavelets in L2(R) are at opposite extremes, in the sense that the Haar wavelet is localized in time but not in frequency, whereas the Shannon wavelet is localized in freqency but not in time. We present a rich setting where the Haar and Shannon wavelets coincide and are localized both in time and in frequency. More generally, if R is replaced by a grou...

<p style='text-indent:20px;'>Caputo derivative operational matrices of the arbitrary scaled Legendre and Chebyshev wavelets are introduced by deriving directly from these wavelets. The Caputo used in quadratic optimization systems having fractional or integer orders differential equations. Using matrices, a new programming wavelet-based method without doing any integration operation for f...

Cognitive Architectures (CAs) are the core of artificial cognitive systems. A CA is supposed to specify the human brain at a level of abstraction suitable for explaining how it achieves the functions of the mind. Over the years a number of distinct CAs have been proposed by different authors and their limitations and potentials were investigated. These CAs are usually classified as symbolic and...