Approximation of Signals by Harmonic-Euler Triple Product Means

Our paper deals with the approximation of signals by <em>H₁.E^θ.E^θ</em> product means of Fourier and its conjugate series. New theorems based on <em>H₁.E^θ.E^θ</em> product summability have been established and proved under general conditions. The established theorems extend, generalize and improve various existing results on summability of Fourier series and its conjugate series.

On Approximation of Signals in the Generalized Zygmund Class Using (E,r)(N,qn) Mean of Conjugate Derived Fourier Series

In the present article, we have established a result on degree of approximation of function in the generalized Zygmund class Zl(m),(l ≥ 1) by (E,r)(N,qn)- mean of conjugate derived Fourier series.

Using the method of moments for the approximation of signals containing peak shaped structural elements

В данной работе производится обобщение метода моментов, предложенного в одной из недавних статей для моделирования зубцов электрокардиограммы комплексами из нескольких функций Гаусса. Цель заключалась в том, чтобы сделать метод применимым для функций более общего вида, сохранив простоту его программной реализации. Для этого был проведен ряд математических преобразований в общем виде и получены достаточно простые соотношения для вычисления параметров модельного сигнала. Это дает возможность применять для аппроксимации участков сигналов функции разнообразного вида, продиктованные их физической моделью. Единственным ограничением для используемых функций является существование необходимого количества моментов, а момент нулевого порядка должен быть отличен от нуля. В данной работе продемонстрировано несколько примеров реализации обобщенного метода моментов. Показано, что на практике в зависимости от вида используемой для моделирования функции возникает ряд вычислительных особенностей, касающихся точности метода и его устойчивости по отношению к шуму. Полученные результаты могут быть полезны для разработки новых эффективных моделей биомедицинских сигналов, атомных и ядерных спектров, а также иных типов сигналов, имеющих локальные особенности в форме пиков. In this paper a generalization of the method of moments which was proposed in a recent article for modeling electrocardiogram waves with sets of several Gauss functions is performed. The purpose is to make the method applicable to functions of a more general form, while maintaining the simplicity of its program implementation. For this a series of mathematical transformations were carried out in a general form and sufficiently simple relations were obtained for calculating the parameters of the model signal. This makes it possible to use functions of various types for the approximation of signal regions, dictated by their physical model. The only restriction for the functions used is the existence of the required number of moments, and the moment of zero order must be different from zero. This paper demonstrates several examples of the implementation of the generalized method of moments. It is shown that in practice, depending on the type of function used for modeling, a number of computational features arise concerning the accuracy of the method and its stability with respect to noise. Obtained results can be useful for developing new effective models of biomedical signals, atomic and nuclear spectra, as well as other types of signals that have peak shaped local features.

Approximation of Signals in the Weighted Zygmund Class Via Euler-hausdorff Product Summability Mean of Fourier Series

Approximation of functions of Lipschitz and zygmund classes have been considered by various researchers under different summability means. In the proposed paper, we have studied an estimation of the order of convergence of Fourier series in the weighted Zygmund class <em>W(Z_r^(ω))</em> by using Euler-Hausdorff product summability mean and accordingly established some (presumably new) results. Moreover, the results obtained here are the generalization of several known results.

Approximation of signals by general matrix summability with effects of Gibbs Phenomenon

In the proposed paper the degree of approximation of signals (functions) belonging to $Lip(\alpha,p_{n})$ class has been obtained using general sub-matrix summability and a new theorem is established that generalizes the results of Mittal and Singh [10] (see [M. L. Mittal and Mradul Veer Singh, Approximation of signals (functions) by trigonometric polynomials in $L_{p}$-norm, \textit{Int. J. Math. Math. Sci.,} \textbf{2014} (2014), ArticleID 267383, 1-6 ]). Furthermore, as regards to the convergence of Fourier series of the signals, the effect of the Gibbs Phenomenon has been presented with a comparison among different means that are generated from sub-matrix summability mean together with the partial sum of Fourier series of the signals.