This paper considers the problem of reconstructing a class of generalized sampled signals of which a special case occurs in, e.g., a generalized sampling system due to non-ideal analysis basis functions. To this end, we propose an improved reconstruction system and a reconstruction algorithm based on generalized inverse, which can be viewed as a reconstruction method that reduces reconstruction error as well. The key idea is to add an additional channel into a generalized sampling system and apply the generalized inverse theory to the reconstruction algorithm. Finally, the approach is applied, respectively, to an oscilloscope, which shows the proposed method yields better performance as compared to the existing technique.

A real narrowband noise signal representation in the form of an analytical signal in the Hilbert space is presented in the paper. This analytical signal is illustrated in a variable complex plane as a mark with defined amplitude, phase, pulsation and instantaneous frequency. A block diagram of a broadband product detector in a quadrature system is presented. Measurement results of an autocorrelation function of a noise signal are shown and the application of such solution in a noise radar for precise determination of distance changes as well as velocities of these changes are also presented. Conclusions and future plans for applications of the presented detection technique in broadband noise radars bring the paper to an end.

An ideal observability subspace expression is stated for bilinear abstract system with bounded operator in Hilbert spaces. The case of finite dimentional space is also treated. However, it’s noticed that the state ideal observability can never be fulfilled within an infinite dimensional phase space in the case of scalar output. The case of bilinear discrete-time system with delays in observation is also described. To illustrate this work some examples are presented.

One of the main problems of electrical power quality is to ensure a constant power ?ux from the supply system to the receiver, keeping in the same time the undisturbed wave form of the current and voltage signals. Distortion of signals are caused by nonlinear or time varying receivers, voltage changes or power losses in a supply system. The wave-form of the voltage of the source may also be deformed. This study seeks the optimal current and voltage wave-form by means of an optimization criteria. The optimization problem is de?ned in Hilbert space and the special functionals are minimized. The source inner impedance operator is linear and time-varying. Some examples of calculations are presented.

Krzysztof Maurin was an extremely versatile intellectual and academic teacher. He worked in mathematics (monograph “Methods of Hilbert space”), philosophy (publication “Karl Jaspers – a philosopher of truthfulness”), theology (essay “The Son of Man as the foundation of great religions”) as well as in psychology and he taught in the Faculty of Physics of the Warsaw University: I was taught by Him during a second half of His life since the beginning of the 70s. Now we are seeing and presenting his various activities in the time analysed by him in senses of quantum and cosmic physics, Heidegger's philosophy, Schweitzer's theology and human and humanitarian psychology. Therefore we remind below his lectures on Medieval Universities, Humboldt's reform, the XIX century mathematics and indeterministic interpretation of quantum mechanics. Then, according to a chronological order, we are switching our attention to Krzysztof Maurin himself as a student of university underground courses during the time do Nazists occupation in Poland, then as a silent university employee resisting communist totalitarian ideology and after 1956, as a methodical professor of the University of Warsaw collaborating with Western Europe scientists such as LDrs GDrding, Werner Heisenberg, Rene Thom and Friedrich von Weizsacker as well as admiring especially intellectual achievements of Hermann Weyl and Martin Heidegger. To the end of biographical considerations we can observe successes and obstacles encountered by Krzysztof Maurin while He has tended to conciliate various or opposite ways of philosophical understanding or social behaving by his beloved thinkers.