Josef Hrusak

On state-space energy based generalization of Brayton-Moser topological approach to electrical network decomposition

This paper deals with generalization of the Brayton–Moser network decomposition and related structural properties to a relatively large class of finite dimensional strictly causal systems, which can be described in the state-space representation form. The resulting energy-metric function is defined for dissipative systems and is induced by the output signal dissipation power. It is demonstrated that such a power-oriented approach determines both, the structure of a system representation as well as the corresponding system state space topology. A special form of physically correct internal structure of an equivalent state space representation has been derived as a natural consequence of strict causality, the state-space energy conservation, dissipativity assumption and the state minimality requirement.

Physical correctness of system representations based on generalized Tellegen principle

The paper deals with a new problem of physical correctness detection in the area of strictly causal system representations. The proposed approach to the problem solution is based on generalization of Tellegens theorem well known from electrical engineering. Consequently, mathematically as well as physically correct results are obtained. The contribution is mainly concerned with presentation of a new structural approach to analysis and synthesis of linear and non-linear causal systems. It has been proven that complete analysis of instability, conservativity, dissipativity, anti-dissipativity, stability, asymptotic stability and chaoticity reduces to two independent tests: the monotonicity test of abstract state space energy and that of complete state observability, evtl. of its dual, i.e. complete state controllability property.

A novel type of mixer used for direct frequency synthesis

The Frequency synthesizers are an essential part of any modern communications system. They generate clock and oscillator signals needed for up and down conversion. Todays communication standards demand both high frequency accuracy and fast frequency settling. The fine frequency resolution is usually desired and low spurious signals, accuracy and stability are also most important for these devices. For some types of the frequency synthesizer the mixer is very significant part. In this paper, the frequency synthesizer architecture based on direct synthesis described. More over the new coincidence mixer used in this synthesizer is presented. The mathematic derivation and simulation results are also shown.

High spectral quality sinusoidal oscillator with energy based amplitude control

This paper presents a high spectral quality voltage-controlled sinusoidal quadrature oscillator. The amplitude stabilization of the output signal is based on energy approach. Described voltage-controlled oscillator has potential applications phase locked loops in modulation, detection etc. Most of the sinusoidal oscillators available in open literature are suffering with same problem. The amplitude stabilization is based on output saturation or simple nonlinear circuit which leads to sine wave distortion and therefore generation of spurious spectral lines. So this paper describes new principle of amplitude stabilization based on energy approach and verifies the results by simulation.

Feedback systems with memristors

The contribution is concerned on the properties of the new ideal circuit element, a memristor. By definition, a memristor relates the charge q and the magnetic flux ¿ in a circuit, and complements a resistor R, a capacitor C, and an inductor L as an ingredient of ideal electrical circuits. The properties of these three elements and their circuits are a part of the standard curricula. The existence of the memristor as the fourth ideal circuit element was predicted in 1971 based on symmetry arguments, but was clearly experimentally demonstrated in 2008. The definition of the memristor is based solely on fundamental circuit variables, similar to the resistor, capacitor, and inductor. Unlike those more familiar elements, the necessarily nonlinear memristors may be described by any of a variety of time-varying functions. As a result, memristors do not belong to linear time-invariant circuit models. A linear time-invariant memristor is simply a conventional resistor.

Comparing frequency domain, optimal, and asymptotic filtering: a tutorial

This paper studies some connections between the main results of the Kalman-Bucy stochastic approach to filtering problems based mainly on linear stochastic estimation theory and emphasizing the optimality aspects of the achieved results and the classical deterministic frequency domain linear filters (such as Chebyshev, Butterworth, Bessel, etc.). A new non-stochastic but not necessarily deterministic (possibly nonlinear) alternative approach to signal filtering based mainly on concepts of signal power, signal energy, and an equivalence relation plays a dominant role in the presentation. Causality, error invariance, and especially error convergence properties are the most important and fundamental features of resulting filters. Therefore, it is natural to call them asymptotic filters. Although error convergence aspects are emphasized in the approach, it is shown that introducing the signal power as the quantitative measure of signal energy dissipation makes it possible to achieve reasonable results from the optimality point of view as well. The authors show that the notion of the asymptotic filter can be used as a proper tool for unifying stochastic and non-stochastic, linear and nonlinear approaches to signal filtering.

Generalization of Nonlinear Observer Design Via Dissipation Normal Form

Abstract State reconstruction is one of fundamental areas investigated in the system theory and a lot of articles have been already dedicated to it in technical literature. The generalization of nonlinear observer design via dissipation normal form considered in the paper represents a fully new approach to the solution of the observer design problem for nonlinear systems. As the theoretical base of this approach the well-known dissipation system theory which allows fulfilling natural demands for the observer design very well has been chosen.

Nonlinear stabilization of oscillators by state space energy error feedback

Computation complexity of a broad variety of practical design problems is known to be strongly depending on an imagination about the particular real-world situation. The contribution is based on the fact that our knowledge of reality is always incomplete. The proposed approach is based on the idea that new knowledge can be gained by comparison using the requirement of consistency of different physical, mathematical and system-theoretic interpretations. In this paper the new approach is proposed for control of energy in sinusoidal and chaotic oscillators.

Analog-digital coincidence mixer for frequency synthesizers

In this paper, a frequency synthesizer architecture is proposed, employing a new analog-digital mixer based on signal coincidence, which achieves fast-settling, and high resolution compared with the conventional synthesizer. This new coincidence mixer, using digital error correction techniques, requires no output filters where sum and difference of input signal frequencies are obtained directly by separated outputs. The examples, related to new synthesizer are also presented. The new coincidence mixer is also realized and the measuring results are also given.

Wavelets filter banks based on continuous-time asymptotic filters

Digital signal processing has played a key role in development of telecommunication systems over the last decade. In recent years digital filter banks have been occupying an increasingly important role in wireless and wireline communication systems. In some applications it is necessary to use filter banks which are not uniform. These decompose a given spectrum into sub-spectra of different bandwidths. Filter banks with exponentially spaced center frequencies and bandwidths are of particular interest. The best known examples of this type are octave filter banks, which are considered here. Closely related to these are dyadic wavelets, which are transformation kernels used for multiresolution analysis of non-stationary signals, the so-called wavelet analysis. In this paper an obvious and straightforward idea of wavelet transform construction and building of the corresponding digital filter bank based on a class of finite order error signal energy optimal IIR filters called asymptotic filters are presented and illustrated by simulation