Introduction to signal processing: sine wave and complex signals

Abstract

The article describes one of the powerful tools for the signals analysis while transmission – complex mathematics. Here the basic concepts (complex numbers, complex signal as expansion of a real signal to a complex-valued function) and some operations (exponentiation, absolute value and angular phase representation) are introduced. As an example complex mathematical methods are used for the case of classical electrical circuits with resistors, capacitors, coils. Actions can be performed both analytically and on a computer, using, for example, MatLab or any other computing software. Illustrations of the signal passage through electrical circuits are supplied with a commented Matlab code, which is used to their producing. The article is supposed to be used as a teaching aid, for self-learning the basics of the signal processing. It is considered as a first introduction part of a series on modern signal processing technologies. Three main approaches to the exploring of the case are also demonstrated: ideological (experiment and its principal explanation), mathematical and computer modeling.