Digital predistortion is a signal processing technique used to remove undesired distortions caused by nonlinear system effects. This method is predominately used to linearize power amplifiers in communication systems in order to achieve efficient transmitter circuits. However, the technique can readily be applied to cancel undesired nonlinear behavior in other types of systems. This thesis investigates the effectiveness of digital predistortion in the context of a wideband arbitrary waveform generator. A theoretical foundation discussing nonlinear system models, predistortion architectures and system identification methods is complemented with a simulation study and followed by verification on a real system. The best predistorter is able to fully suppress the undesired distortions for any fixed two-tone sinusoidal signal. Furthermore, the results indicate the existence of a wideband predistorter which yield acceptable suppression over a frequency range of several hundred MHz. / Digital predistorsion är en signalbehandlingsteknik som används för att undertrycka oönskade distorsioner orsakade av icke-linjära effekter i elektriska system. Denna metod används i huvudsak för att linjärisera effektförstärkare i kommunikationssystem för att erhålla effektiva sändarkedjor men tekniken kan utan större problem även tillämpas på andra typer av icke-linjära system. Denna uppsats undersöker i vilken utsräckning digital predistorsion kan användas för att undertrycka oönskade signaldistorsioner i en bredbandig signalgenerator. Uppsatsen presenterar en bakgrund som utgår ifrån teorin om icke-linjära systemmodeller, arkiteturer för predistorsion och systemidentifieringsmetoder. En kvantitativ studie i en simuleringsmiljö åtföjs av en utvärdering på ett verkligt system. Det bästa predistorsionssystemet åstadkommer en fullständig linjärisering i testfallet med en fix tvåtonssignal. Resultaten indikerar även att det existerar ett system som linjäriserar signaler i ett frekvensområde som uppgår till hundratals MHz.

The extensive use of a least-squares problem formulation in many fields is partly motivated by the existence of an analytic solution formula which makes the theory comprehensible and readily applicable, but also easily embedded in computer-aided design or analysis tools. While the mathematics behind convex optimization has been studied for about a century, several recent researches have stimulated a new interest in the topic. Convex optimization, being a special class of mathematical optimization problems, can be considered as generalization of both least-squares and linear programming. As in the case of a linear programming problem there is in general no simple analytical formula that can be used to find the solution of a convex optimization problem. There exists however efficient methods or software implementations for solving a large class of convex problems. The challenge and the state of the art in using convex optimization comes from the difficulty in recognizing and formulating the problem. The main goal of this thesis is to investigate the potential advantages and benefits of convex optimization techniques in the field of system identification. The primary work focuses on parametric discrete-time system identification models in which we assume or choose a specific model structure and try to estimate the model parameters for best fit using experimental input-output (IO) data. By developing a working knowledge of convex optimization and treating the system identification problem as a convex optimization problem will allow us to reduce the uncertainties in the parameter estimation. This is achieved by reecting prior knowledge about the system in terms of constraint functions in the least-squares formulation.

In part one we show that for a compact, metric, locally path-connected topological space X, the shape group of X - as defined in Foundations of Shape Theory by Mardesic and Segal - is isomorphic to the inverse limit of discrete homotopy groups introduced by Conrad Plaut and Valera Berestovskii. We begin by providing the reader preliminary definitions of the fundamental group of a topological space, inverse systems and inverse limits, the Shape Category, discrete homotopy groups, and culminate by providing an isomorphism of the shape and deck groups for peano continua. In part two we develop work and provide further classification of Sharkovskii topological groups, which we call Sharkovskii Groups. We culminate in proving the fact that a locally compact Sharkovskii group must either be the real numbers if it is not compact, or a torsion-free solenoid if it is compact.