A countable collection X of functions in L2(IR ) is said to be a Bessel system if the associated analysis operator T ∗ X : L2(IR ) → `2(X) : f 7→ (〈f, x〉)x∈X is well-defined and bounded. A Bessel system is a fundamental frame if T ∗ X is injective and its range is closed. This paper considers the above two properties for a generalized shift-invariant system X. By definition, such a system has t...

Methods for detecting and quantifying nonlinearities in nonstationary time series are introduced and developed. In particular, higher-order wavelet analysis was applied to an ideal time series and the quasi-biennial oscillation (QBO) time series. Multiple-testing problems inherent in wavelet analysis were addressed by controlling the false discovery rate. A new local autobicoherence spectrum fa...

In this paper, local cubic quasi-interpolating splines on non-uniform grids are described. The splines are designed 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, the splines use either clean or noised arbitrarily-spaced samples. Formulas for the...

Nonlinear thresholding of wavelet coefficients has been shown to be an efficient method for denoising signals with isolated singularities corrupted with Gaussian white noise. A quasi optimal value for the threshold can be computed from the noise level using the formula TD = σW √ 2 ln N , where N is the number of available samples of the signal and σW is the standard deviation of the noise. Howe...

we present here the numerical solution of damped forced oscillator problem using haar wavelet and compare the numerical results obtained with some well-known numerical methods such as runge-kutta fourth order classical and taylor series methods. numerical results show that the present haar wavelet method gives more accurate approximations than above said numerical methods.

Discrete wavelet transform is a useful means for crack identification of beam structures. However, its accuracy severely dependent on the selecting mother and vanishing moments, which raises significant challenge in practical structural identification. In this paper, novel approach introduced health monitoring beams to fix challenge. The based combination statistical characteristics vibrational...

In this article, we consider fast direct solvers for nonlocal operators. The pivotal idea is to combine a wavelet representation of the system matrix, yielding quasi-sparse with nested dissection ordering scheme. latter drastically reduces fill-in during factorization matrix by means Cholesky decomposition or an LU decomposition, respectively. This way, end up exact inverse compressed only mode...

We propose invariant formulations that can potentially be combined into a single system. In particular, we describe a framework for computing invariant features which are insensitive to rigid motion, a ne transform, changes of parameterization and scene illumination, perspective transform, and view point change. This is unlike most current research on image invariants which concentrates on eith...

D epartement de math ematiques Universit e du Qu ebec a Montr eal 0 PRELIMINARIES 1 Abstract One important challenge in non{parametric density and regression{function estimation is spatially inhomogeneous smoothness. This is often modelled by Besov-and Triebel{type smoothness constraints. Donoho and Johnstone (1992), Delyon and Juditsky (1993) studied minimax rates of convergence for wavelet es...