A system is differentially flat if it is Lie–Bäcklund (L-B) equivalent to a free dynamical system that has dimensions equal to that of the input of the original system. Utilizing this equivalence, the problem of nonlinear model predictive control of a flat system can be reduced to a lower dimensional nonlinear programming problem with respect to the flat outputs. In this work, a novel computati...

Wavelet shrinkage (WaveShrink) is a relatively new technique for nonparametric function estimation that has been shown to have asymptotic near-optimality properties over a wide class of functions. As originally formulated by Donoho and Johnstone, WaveShrink assumes equally spaced data. Because so many statistical applications (e.g., scatterplot smoothing) naturally involve unequally spaced data...

Nowadays, each newly produced car must conform to the appropriate safety standards and norms. The most direct way to observe how a car behaves during a collision and to assess its crashworthiness is to perform a crash test. This paper deals with the wavelet-based performance analysis of the safety barrier for use in a full-scale test. The test involves a vehicle, a Ford Fiesta, which strikes th...

Let M be an n × n matrix with i.i.d. CN(0, 1) entries (Complex Normal random variables with mean 0 and variance 1), and define A = M +M ∗ √ 2 , where M∗ denotes the conjugate transpose of M . The resulting random matrix is a member of the Gaussian Unitary Ensemble (GUE), and we would like to classify the distribution of its eigenvalues. In a previous section, the measure of the Gaussian Unitary...

We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in three equivalent forms: as a determinant sum (and hence in terms of symmetric polynomials), as a combinatorial sum, and as a multiple contour integral. These...

In this paper, a minimization of Haar wavelet series for simplification of circuits and Haar based decision diagrams representing discrete multiple-valued functions is proposed. The minimization is performed by permutation of indices of generalized Haar functions. Experimental results show that this method provides reasonable reduction in the number of non-zero coefficients. The Haar series red...

We give a new generalization for Haar functions. The generalization starts from the Walsh-like functions and based on the connection between the original Walsh and Haar systems. We generalize the Haar– Fourier Transform too.

In this article,we present a wavelet method for solving stochastic Volterra integral equations based on Haar wavelets. First, we approximate all functions involved in the problem by Haar Wavelets then, by substituting the obtained approximations in the problem, using the It^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation w...

The new class of weights called A p weights is introduced. We prove that a characterization and an unconditional basis of the weighted Lp space Lp(Rn,w(x)dx) with w ∈ A p (1 < p < ∞) are given by the Haar wavelets and the Haar scaling function. As an application of these results, we establish a greedy basis by using the Haar wavelets and the Haar scaling function again.