Bulletin of the Polish Academy of Sciences Technical Sciences

Extraction of the foetal electrocardiogram from single-channel maternal abdominal signals without disturbing its morphology is difficult. We propose to solve the problem by application of projective filtering of time-aligned ECG beats. The method performs synchronization of the beats and then employs the rules of principal component analysis to the desired ECG reconstruction. In the first stage, the method is applied to the composite abdominal signals, containing maternal ECG, foetal ECG, and various types of noise. The operation leads to maternal ECG enhancement and to suppression of the other components. In the next stage, the enhanced maternal ECG is subtracted from the composite signal, and this way the foetal ECG is extracted. Finally, the extracted signal is also enhanced by application of projective filtering. The influence of the developed method parameters on its operation is presented.

One of the prime tool in non-invasive cardiac electrophysiology is the recording of an electrocardiographic signal (ECG) which analysis is greatly useful in the screening and diagnosis of cardiovascular diseases. However, one of the greatest problems is that usually recording an electrical activity of the heart is performed in the presence of noise. The paper presents Bayesian and empirical Bayesian approach to problem of weighted signal averaging in time domain which is commonly used to extract a useful signal distorted by a noise. The averaging is especially useful for biomedical signal such as ECG signal, where the spectra of the signal and noise significantly overlap. Using the methods of weighted averaging are motivated by variability of noise power from cycle to cycle, often observed in reality. It is demonstrated that exploiting a probabilistic Bayesian learning framework leads to accurate prediction models. Additionally, even in the presence of nuisance parameters the empirical Bayesian approach offers the method of theirs automatic estimation which reduces number of preset parameters. Performance of the new method is experimentally compared to the traditional averaging by using arithmetic mean and weighted averaging method based on criterion function minimization.

A new class of positive hybrid linear systems is introduced. The solution of the hybrid system is derived and necessary and sufficient condition for the positvity of the class of hybrid systems are established. The classical Cayley-Hamilton theorem is extended for the hybrid systems. The reachability of the hybrid system is considered and sufficient conditions for the reachability are established. The considerations are illustrated by a numerical example.

In the paper an application of differential evolution algorithm to design digital filters with non-standard amplitude characteristics is presented. Three filters with characteristics: linearly growing, linearly falling, and non-linearly growing are designed with the use of the proposed method. The digital filters obtained using this method are stable, and their amplitude characteristics fulfill all design assumptions.

The main objective of this work is to provide a closed formula for the backward and symmetric solution of the 2-D implicit Roesser model. The relative forward and backward fundamental matrix is of fundamental importance in our approach. An algorithm for the

determination of the backward fundamental matrix sequense is also given.

The paper discusses the stability problem for continuous time and discrete time positive systems. An alternative formulation of stability criteria for positive systems has been proposed. The results are based on a theorem of alternatives for linear matrix inequality (LMI) feasibility problem, which is a particular case of the duality theory for semidefinite programming problems.

Two-dimensional (2D) positive systems are 2D state-space models whose state, input and output variables take only nonnegative values. In the paper we explore how linear matrix inequalities (LMIs) can be used to address the stability problem for 2D positive systems. Necessary and sufficient conditions for the stability of positive systems have been provided. The results have been obtained for most popular models of 2D positive systems, that is: Roesser model, both Fornasini-Marchesini models (FF-MM and SF-MM) and for the general model.

The standard approach to the wave propagation in an inhomogeneous elastic layer leads to the displacement in a form of a product of a function of space and a harmonic function of time. This product represents the standing, and not the running wave. The part depending on the space variable is governed by the linear ordinary second order differential equation. In order to calculate the propagation speed in the present paper the inhomogeneous material is separated by a plane into two parts. Between the two inhomogeneous parts the virtual homogeneous elastic extra layer is added. The elasticity modulus and the mass density of the extra layer have the same values as the inhomogeneous material on the separation plane. In further calculations the extra layer is assumed to be infinitesimally thin. The virtual layer allows to decompose the motion into two waves: a wave running to the right and a wave running to the left. Energy conservation equation is derived.

The paper explains the force induced by the electrostatic field on the electron as a recoil force. The starting point is the hypothesis that in the dynamic equilibrium with the vacuum, the electron simultaneously absorbs and emitts energy. With no external electrostatic field the radiation patterns of absorption and emission are assumed to be isotropic. The external electrostatic field induces anisotropy of the emission resulting in a recoil force. The paper presents a theoretical description of this force using a model of the angular power density pattern of the emission in the form of an ellipsoid. Calculations show that the total radiated power is extremely high. This radiation is compared with the electromagnetic radiation of the electron on the Bohr orbit in the idealized hydrogen atom. An analogous problem for gravitational forces is presented.

The paper presents the theoretical background, computer model, laboratory measurements and SPICE simulation results of a 323 W, 1 MHz Class E inverter operating with an efficiency of 97%. The inverter is built around a CoolMOS transistor from Infineon Technologies. The transistor belongs to a new generation of high quality, optimized for low conduction losses and high speed switching power MOSFET-s. The presented computer model of Class E inverter is based on a state-space description and allows computing the inverter parameters for the optimum operation. Its validity has been confirmed experimentally. The SPICE simulation of the inverter has been also carried out in order to obtain better agreement between measurement and calculation results.

A novel current-inversion type negative impedance converter (CNIC) is presented. It is built without the use of any resistors. Furthermore, a second-order low-pass filter based on this CNIC is also analysed. It shows a bandwidth of 50 MHz at 320 µW power consumption and 2 V supply voltage when realized in a 0.35 µm CMOS process.