2.2 FUNDAMENTALS OF ANALOG SIGNALS

Regardless of whether they are transmitted in analog or digital form, the signals encountered in communications systems are often highly complex. A spoken sentence, a piece of music, a television picture, or a stream of digital data all vary continuously with time and may contain thousands—or even millions—of individual variations every second. Attempting to analyze such signals directly would be extremely difficult, making it challenging to predict how they will behave when transmitted through a communications system.

Fortunately, one of the most powerful results in mathematics and engineering shows that even the most complicated waveform can be represented as the sum of a number of much simpler waveforms known as sinusoids (or sine waves). Each sinusoid has a well-defined frequency, amplitude, and phase, and its behavior is straightforward to describe mathematically. Rather than attempting to understand a complicated signal all at once, engineers analyze its individual sinusoidal components and then combine the results to determine the behavior of the complete signal. This approach is analogous to understanding a complex musical chord by identifying the individual notes that compose it.

This seemingly simple idea forms the basis of an enormous amount of modern communications engineering. It underpins the analysis of electrical circuits, radio transmission, signal filtering, modulation, multiplexing, antennas, optical communications, and digital signal processing. Techniques such as Fourier analysis, which are introduced later in this chapter, rely entirely on the principle that complex signals can be decomposed into simpler sinusoidal components.

Consequently, understanding the properties of a single sinusoid provides the foundation for understanding almost every communications system encountered in this book. Before considering more complicated signals, we therefore begin with the simplest possible waveform and examine its properties in detail. Once these basic building blocks have been established, they can be combined to analyze the much richer signals used in practical communications systems.