Luis J. Morales-Mendoza

FIR Smoothing of Discrete-Time Polynomial Signals in State Space

We address a smoothing finite impulse response (FIR) filtering solution for deterministic discrete-time signals represented in state space with finite-degree polynomials. The optimal smoothing FIR filter is derived in an exact matrix form requiring the initial state and the measurement noise covariance function. The relevant unbiased solution is represented both in the matrix and polynomial forms that do not involve any knowledge about measurement noise and initial state. The unique l-degree unbiased gain and the noise power gain are derived for a general case. The widely used low-degree gains are investigated in detail. As an example, the best linear fit is provided for a two-state clock error model.

Universal character of the fractional space-time electromagnetic waves in dielectric media

This work presents an alternative solution for the mathematical analysis of the fractional waves in dielectric media. For the fractional wave equation, the Caputo fractional derivative was considered, the order of the spatial and temporal fractional derivatives are , respectively. In this analysis, we introduce the appropriate fractional dimensional parameters which characterize consistently the existence of the fractional space and time derivatives into the fractional wave equation. We will consider source free Maxwell equations in isotropic and homogeneous dielectric medium. The general solutions obtained in our research have been expressed in terms of the multivariate Mittag–Leffler functions, these functions depend only on the parameters and preserving the appropriated physical units according to the system studied.

A new class of discrete orthogonal polynomials for blind fitting of finite data

We show that the polynomial unbiased finite impulse response (UFIR) functions derived by Shmaliy establish a new class of a one-parameter family of discrete orthogonal polynomials (DOP). Unlike the classical finite-data DOP, the UFIR polynomials depend on only one parameter - the length of finite data. This makes them highly attractive for L-order blind fitting and representation of informative processes. Examples of applications are given for voice phoneme analysis and approximation in a comparison with the Hahns polynomials.

Moving Average Hybrid FIR Filter in Ultrasound Image Processing

In this work, we present a novel technique for ultrasound image processing (2D signals). The moving average hybrid FIR filter (MAH-FIR) which it work with two different FIR filter, the moving average (MA) and median hybrid (FMH) filters. We experimented with continuous linear regression function and Lagrange multiplier to obtain the approximation of the MA-FIR and FMH-FIR filters, respectively. Furthermore, we showed both filters composed into a block diagram. Finally, we present evaluations qualitative and quantitative of ultrasound image processing.

Experimental evaluation of viscous damping coefficient in the fractional underdamped oscillator

In this article, we obtain the viscous damping coefficient β theoretically and experimentally in the spring–mass–viscodamper system. The calculation is performed to obtain the quasi-period τ. The influence of the viscosity of the fluid and the damping coefficient is analyzed using three fluids, water, edible oil, and gasoline engine oil SAE 10W-40. These processes exhibit temporal fractality and non-local behaviors. Our general non-local damping model incorporates fractional derivatives of Caputo type in the range ( 0 , 1 ] , and the viscous damping coefficients are determined in terms of the inverse Mittag-Leffler function. The classical models are recovered when the order of the fractional derivatives is equal to 1.

Nonlinearities Distribution Homotopy Perturbation Method Applied to Solve Nonlinear Problems: Thomas-Fermi Equation as a Case Study

We propose an approximate solution of T-F equation, obtained by using the nonlinearities distribution homotopy perturbation method (NDHPM). Besides, we show a table of comparison, between this proposed approximate solution and a numerical of T-F, by establishing the accuracy of the results.

Analytical Solutions for Systems of Singular Partial Differential-Algebraic Equations

This paper proposes power series method (PSM) in order to find solutions for singular partial differential-algebraic equations (SPDAEs). We will solve three examples to show that PSM method can be used to search for analytical solutions of SPDAEs. What is more, we will see that, in some cases, Pade posttreatment, besides enlarging the domain of convergence, may be employed in order to get the exact solution from the truncated series solutions of PSM.

Direct application of Padé approximant for solving nonlinear differential equations

This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant.AMS Subject Classification34L30

P-step unbiased FIR filter to the ultrasound image processing

In this paper we present a new generation of unbiased FIR filter called as p-step unbiased FIR filter. These filters present a computational ability and flexibility to realize three different processes: prediction, filtering and smoothing. Moreover, the medical ultrasound is an interesting area to the applications of p-step unbiased FIR filter type. This is due to the ultrasound images are contaminating with Gaussian and speckle noise. Finally, we present some simulations to prove the new unbiased FIR filters and concluding remarks.

Fractional electromagnetic waves in conducting media

We present the fractional wave equation in a conducting material. We used a Maxwell’s equations with the assumptions that the charge density and current density J were zero, and that the permeability and permittivity were constants. The fractional wave equation will be examined separately; with fractional spatial derivative and fractional temporal derivative, finally, consider a Dirichlet conditions, the Fourier method was used to find the full solution of the fractional equation in analytic way. Two auxiliary parameters and are introduced; these parameters characterize consistently the existence of the fractional space-time derivatives into the fractional wave equation. A physical relation between these parameters is reported. The fractional derivative of Caputo type is considered and the corresponding solutions are given in terms of the Mittag-Leffler function show fractal space-time geometry different from the classical integer-order model.