is the ability to reduce the number of regenerators required on long transmission spans. In a typical network, these regenerators must be placed approximately every 6,000 feet along a span, which means that there is considerable expense involved when providing regeneration along a long-haul network. Digital signals, often called "square waves," have a very rich mixture of signal frequencies. Not to bring too much physics into the discussion, we must at least mention the Fourier Series, which describes the makeup of a digital signal. The Fourier Series is a mathematical repre- sentation of the behavior of waveforms. Among other things, it notes the following fact. If we start with a fundamental signal-such as that shown in Figure 3-65-and mathematically add to it its odd harmonics (a "harmonic" is defined as a wave whose frequency is a whole-number Strong Figure 3-64 Weak, noisy Regenerator Restored Signal signal Signal Role of the regenerator Time and Distance Figure 3-65 Fourier series transform of analog wave to digital wave Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Telephony Telephony multiple of another wave), we see a rather remarkable thing happening: The waveform gets steeper on the sides and flatter on top. As we add more and more of the odd harmonics (there is, after all, an infinite series of them), the wave begins to look like the typical square wave. Now of course, there is no such thing as a true square wave; for our purposes, though, we'll accept the fact. It should now be intuitive to the reader that digital signals have a mixture of low-, medium-, and high-frequency components, which means that they cannot be transmitted across the bandwidth-limited 4 KHz channels of the traditional telephone network. In digital carrier facilities, the equipment that restricts the individual transmission channels to 4 KHz "chunks" is el