Borys A. Analysis and synthesis of nonlinear telecommunication devices and circuits using continuous and discrete Volterra series.

The dissertation is devoted to the analysis and synthesis of analog and digital nonlinear telecommunication circuits and systems with the so-called nonlinearities. The tool used here is the Volterra series; that is its continuous version for analog devices and circuits, and its discrete version for digital ones. The problems of analysis, minimization and elimination of nonlinear distortion in telecommunication circuits and systems are addressed. Moreover, a method and effective algorithms of a computer program for calculation of nonlinear distortion in sinusoidal oscillators are presented, too. A large portion of the dissertation is devoted to the analysis of nonlinear echo compensators used in digital transmission systems. Using general structures developed, structures of nonlinear echo compensators for baseband data transition systems has been found. The behavior of these compensators has been analyzed in detail. Similarly, structures of nonlinear echo compensators working in the passband have been developed as well. Moreover, the problems related to the fact that timing recovery in digital transmission systems imposes that the sampling rate at the echo cancellers output has to be higher than the sampling rate as its input have been addressed, too. As a result, structures of echo cancellers in form of interleaved transversal filters have been presented.