Abstract:

This paper is about new educational methods of involvement students into real scientific research project connected with deterministic and random one-dimensional and multidimensional signals simulation. The novelty of the education methods consists in usage of original high-precision and high performance simulation algorithms of signals generation with proper attributes within the classical theory of correlation in the Fourier and Hartley spectral domain bases. Few original algorithmic relationship models of the pseudo-random and deterministic signals allow students to build general simulation algorithms using common mathematical and software tool, as well as provide teachers with efficient teaching research tool in real-time systems like practical classes and laboratory works. Students solve these scientific and technical tasks, making decision on the main conditions for the reproduction of deterministic or random, univariate and multivariate processes with different characteristics needs to be chosen. During practical research the students understand how the various kinds of interference, noise and distortion effect on the quality of signals.

The real-time information education systems (modeling system) has certain requirements for accuracy, easy setup on specified characteristics and time of simulation. Comparing new approach with existing classic simulation algorithms using in statistical studies based on methods of filter's forming and on canonical decompositions the last ones do not satisfy all the stated requirements. Simplification of the signals simulation algorithms leads to a simplification of the common models of control systems. The novelty of the proposed in these paper solutions is the usage of the original system of basis functions (generalized functions Hartley, for example) to synthesize simulation algorithms, which exceeding known accuracy, simplify settings and reduce computational complexity.

So this paper is about the new methodology of students teaching in the framework of real scientific project. Students do their research on a possibilities of original algorithms and spectral methods of deterministic and random one- and multi-dimensional real-time signals simulation. An example is given about how the students could achieve needed signal’s characteristics by variation of spectral density and correlation function’s parameters. Students do their research using MathLab.

Keywords:

Real-time education system, Hartley bases, Fourier Bases, rules for practical tasks generation, signal simulation.