Signals and Systems/Introduction

What is this book for?

The purpose of this book is to begin down the long and winding road of Electrical Engineering. Previous books on electric circuits have laid a general groundwork, but again: that is not what electrical engineers usually do with their time. Very complicated integrated circuits exist for most applications that can be picked up at a local circuit shop or hobby shop for pennies, and there is no sense creating new ones. As such, this book will most likely spend little or no time discussing actual circuit implementations of any of the structures discussed. Also, this book will not stumble through much of the complicated mathematics, instead opting to simply point out and tabulate the relevant results. What this book will do, however, is attempt to provide some insight into a field of study that is considered very foreign and arcane to most outside observers. This book will be a theoretical foundation that future books will build upon. This book will likely not discuss any specific implementations (no circuits, transceivers, filters, etc...), as these materials will be better handled in later books.

Who is this book for?

This book is designed to accompany a second year of study in electrical engineering at the college level. However, students who are not currently enrolled in an electrical engineering curriculum may also find some valuable and interesting information here. This book requires the reader to have a previous knowledge of differential calculus, and assumes familiarity with integral calculus as well. Barring previous knowledge, a concurrent course of study in integral calculus could accompany reading this book, with mixed results. Using Laplace Transforms, this book will avoid differential equations completely, and therefore no prior knowledge of that subject is needed.

Having a prior knowledge of other subjects such as physics (wave dynamics, energy, forces, fields) will provide a deeper insight into this subject, although it is not required. Also, having a mathematical background in probability, statistics, or random variables will provide a deeper insight into the mechanics of noise signals, but that also is not required.

What will this book cover?

This book is going to cover the theory of LTI systems and signals. This subject will form the fundamental basis for several other fields of study, including signal processing, Digital Signal Processing, Communication Systems, and Control Systems.

This book will provide the basic theory of LTI systems and mathematical modeling of signals. We will also introduce the notion of a stochastic, or random, process. Random processes, such as noise or interference, are so common in the studies of these systems that it's impossible to discuss the practical use of filter systems without first discussing noise processes.

Later sections will introduce some more advanced topics, such as digital signals and systems, and filters. This book will not discuss these topics at length, however, preferring to direct the reader to more comprehensive books on these subjects.

This book will attempt, so far as is possible, to provide not only the materials but also discussions about the importance and relevance of those materials. Because the information in this book plays a fundamental role in preparing the reader for advanced discussions in other books.

Where to go from here

Once a basic knowledge of signals and systems has been learned, the reader can then take one of several paths of study.

• Readers interested in the use of electric signals for long-distance communications can read Communication Systems and Communication Networks. This path will culminate in a study of Data Coding Theory.

• Readers more interested in the analysis and processing of signals would likely be more interested in reading about Signal Processing and Digital Signal Processing. These books will focus primarily on the "signals".

• Readers who are more interested in the use of LTI systems to exercise control over systems will be more interested in Control Systems. This book will focus primarily on the "systems".

All three branches of study are going to share certain techniques and foundations, so many readers may find benefit in trying to follow the different paths simultaneously.