Digital Communications with Emphasis on Data Modems

1MATHEMATICAL BACKGROUND AND ANALYSIS TECHNIQUES

1.1 INTRODUCTION

This introductory chapter focuses on various mathematical techniques and solutions to practical problems encountered in many of the following chapters. The discussions are divided into three distinct topics: deterministic signal analysis involving linear systems and channels; statistical analysis involving probabilities, random variables, and random processes; miscellaneous topics involving windowing functions, mathematical solutions to commonly encountered problems, and tables of commonly used mathematical functions. It is desired that this introductory material will provide the foundation for modeling and finding practical design solutions to communication system performance specifications. Although this chapter contains a wealth of information regarding a variety of topics, the contents may be viewed as reference material for specific topics as they are encountered in the subsequent chapters.

This introductory section describes the commonly used waveform modulations characterized as amplitude modulation (AM), phase modulation (PM), and frequency modulation (FM) waveforms. These modulations result in the transmission of the carrier‐ and data‐modulated subcarriers that are accompanied by negative frequency images. These techniques are compared to the more efficient suppressed carrier modulation that possesses attributes of the AM, PM, and FM modulations. This introduction concludes with a discussion of real ...