This paper is an examination of techniques for obtaining Fourier series-like expansions of finite-energy signals using so-called Gabor and wavelet expansions. These expansions decompose a given signal into time and frequency localized components. The theory of frames in Hilbert spaces is used as a criteria for determining when such expansions are good representations of the signals. Some result...

In this paper we show that wavelets can be used as basis functions for Galerkin methods. For differential equations, finite element or finite difference methods lead to matrices that are already shown to be sparse, but they tend to be ill-conditioned, [4]. In this paper, we show that wavelet basis gives sparse matrix with low condition number for Galerkin methods. Numerical examples are present...

graham higman has defined coset diagrams for psl(2,ℤ). these diagrams are composed of fragments, and the fragments are further composed of two or more circuits. q. mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...

Motivated by recent developments in the study of finitedimensional frames, this work develops an independent theory of finitedimensional wavelet systems on the circle. Using natural translation and dilation operators, trigonometric polynomial, orthonormal scaling functions are constructed which give rise to finite-dimensional multiresolution analyses and, consequently, orthonormal wavelet syste...

The Feichtinger conjecture is considered for three special families of frames. It is shown that if a wavelet frame satisfies a certain weak regularity condition, then it can be written as the finite union of Riesz basic sequences each of which is a wavelet system. Moreover, the above is not true for general wavelet frames. It is also shown that a sup-adjoint Gabor frame can be written as the fi...

This paper presents the application of radial basis neural networks to the development of a novel method for the condition monitoring and fault diagnosis of synchronous generators. In the proposed scheme, flux linkage analysis is used to reach a decision. Probabilistic neural network (PNN) and discrete wavelet transform (DWT) are used in design of fault diagnosis system. PNN as main part of thi...

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...