Complex Envelope Based Modems: A Tutorial

The complex envelope or baseband-equivalent representation of passband functions is a well-developed theory, known to provide elegant and, in most cases, eased mathematical tractability to the analyzes of signals and systems. Although this theory is covered extensively in many textbooks, there are hidden concepts and applications of it, for example related to the fast simulation of communication systems and to the fundamentals for developing software-defined radios. This tutorial exposes these concepts using a differentiated didactic approach, aiming at contributing to the understanding about how to model, simulate and implement modems based on the complex envelope theory.