A sequence of increasing translation invariant subspaces can be defined by the Haar-system (or generally by wavelets). The orthogonal projection to the subspaces generates a decomposition (multiresolution) of a signal. Regarding the rate of convergence and the number of operations, this kind of decomposition is much more favorable then the conventional Fourier expansion. In this paper, starting...

Contents Preface ix 1. Wavelet and frame transforms originated from continuous and discrete splines, Amir Z. Averbuch and Valery A. Zheludev 1 1.1. Introduction 1 1.2. Preliminaries 4 1.3. Prediction filters originated from splines 9 1.4. Biorthogonal wavelet transforms generated by filter banks with downsampling factor N = 2 (diadic transforms) 17 1.5. Application of spline-based wavelet trans...

This paper deals with Szegö type limits for multiplication operators on L(R) with respect to Haar orthonormal basis. Similar studies have been carried out by Morrison for multiplication operators Tf using Walsh System and Legendre polynomials [14]. Unlike the Walsh and Fourier basis functions, the Haar basis functions are local in nature. It is observed that Szegö type limit exist for a class o...

There is an apparent renewed interest in application of the Haar wavelet transform in switching theory and logic design.1–6 In particular, the discrete Haar transform appears very interesting for its wavelets-like properties and fast calculation algorithms. The applications have been found in circuit synthesis, verification and testing.1–9 For applications of the Haar transform in logic design,...

An approximate equivalence checking method is developed based on the use of partial Haar spectral diagrams (HSDs). Partial HSDs are defined and used to represent a subset of the Haar spectral coefficients for two functions. Due to the uniqueness properties of the Haar transform, a necessary condition for equivalence is that the individual coefficients must have the same value. The probability t...

In the present paper we study quasi-Monte Carlo methods to integrate functions representable by generalized Haar series in high dimensions. Using (t; m; s)-nets to calculate the quasi-Monte Carlo approximation, we get best possible estimates of the integration error for practically relevant classes of functions. The local structure of the Haar functions yields interesting new aspects in proofs ...

The present study investigates the Haar-Sinc collocation method for the solution of the hyperbolic partial telegraph equations. The advantages of this technique are that not only is the convergence rate of Sinc approximation exponential but the computational speed also is high due to the use of the Haar operational matrices. This technique is used to convert the problem to the solution of linea...