O matematice v mobilu
On discrete Fourier analysis of amplitude and phase modulated signals
In this work the problem of characterization of the Discrete Fourier Transform (DFT) spectrum of an original complex-valued signal , t=0,1,...,n-1, modulated by random fluctuations of its amplitude and/or phase is investigated. It is assumed that the amplitude and/or phase of the signal at discrete times of observation are distorted by realizations of uncorrelated random variables or randomly permuted sequences of complex numbers. We derive the expected values and bounds on the variances of such...
On generalized methods of the transfer of conditions
The methods of the transfer of conditions are generalized so that they also cover the direct methods leading to the diagonalization of the original matrix of a system with a band matrix. Part 3 is devoted to the numerical stability of methods of the transfer of conditions described in author's previous paper. Finally, it is shown how to obtain a particular method by the choice parameters of the general algorithm.
On High Precision Methods for the Evaluation of Fourier Integrals with Finite and Infinite Limits.
On highly oscillatory problems arising in electronic engineering
In this paper, we consider linear ordinary differential equations originating in electronic engineering, which exhibit exceedingly rapid oscillation. Moreover, the oscillation model is completely different from the familiar framework of asymptotic analysis of highly oscillatory integrals. Using a Bessel-function identity, we expand the oscillator into asymptotic series, and this allows us to extend Filon-type approach to this setting. The outcome is a time-stepping method that guarantees ...
On integer sequences associated with the cyclic and complete graphs.
On multiscale denoising of spherical functions: basic theory and numerical aspects.
On numerical evaluation of integrals involving Bessel functions
On orthonormal product systems.
On some transforms of trigonometric series.
On the computation of scaling coefficients of Daubechies' wavelets
In the present paper, Daubechies' wavelets and the computation of their scaling coefficients are briefly reviewed. Then a new method of computation is proposed. This method is based on the work [7] concerning a new orthonormality condition and relations among scaling moments, respectively. For filter lengths up to 16, the arising system can be explicitly solved with algebraic methods like Gröbner bases. Its simple structure allows one to find quickly all possible solutions.
On the computation of the GCD of 2-D polynomials
The main contribution of this work is to provide an algorithm for the computation of the GCD of 2-D polynomials, based on DFT techniques. The whole theory is implemented via illustrative examples.
On the discrete harmonic wavelet transform.
On the exact values of coefficients of coiflets
In 1989, R. Coifman suggested the design of orthonormal wavelet systems with vanishing moments for both scaling and wavelet functions. They were first constructed by I. Daubechies [15, 16], and she named them coiflets. In this paper, we propose a system of necessary conditions which is redundant free and simpler than the known system due to the elimination of some quadratic conditions, thus the construction of coiflets is simplified and enables us to find the exact values of the scaling coefficients...
On the relationship between quasi-affine systems and the à trous algorithm.
We seek to demonstrate a connection between refinable quasi-affine systems and the discrete wavelet transform known as the à trous algorithm. We begin with an introduction of the bracket product, which is the major tool in our analysis. Using multiresolution operators, we then proceed to reinvestigate the equivalence of the duality of refinable affine frames and their quasi-affine counterparts associated with a fairly general class of scaling functions that includes the class of compactly supported...
On-line wavelet estimation of Hammerstein system nonlinearity
A new algorithm for nonparametric wavelet estimation of Hammerstein system nonlinearity is proposed. The algorithm works in the on-line regime (viz., past measurements are not available) and offers a convenient uniform routine for nonlinearity estimation at an arbitrary point and at any moment of the identification process. The pointwise convergence of the estimate to locally bounded nonlinearities and the rate of this convergence are both established.