input 44,100 times per second, its Nyquist frequency is 22.05 kHz. Our telephone PCM systems sample their audio 8000 times per second, so their Nyquist frequency is 4000 Hz, more than adequate for the 300- to 3300- Hz frequency range of a telephone voice signal. It is important that the audio input be filtered carefully to stay within the Nyquist range. At a sampling rate of S, the audio output has no way of telling frequency f from frequency ks + f or ks - f, for k = 1, 2, All these frequencies will have the exact same values in the stored samples. The term for this incorrect mapping of frequencies is aliasing. In our telephony example of 8000 samples per second, a 5000-Hz component of the audio signal samples the same as a 3000-Hz component and plays back as 3000 Hz. This can be a very annoying distortion, and we employ antialiasing filters to make sure that the audio input bandwidth stays within the Nyquist limits. The Nyquist frequency is an unattainable upper limit for sampling theory the same way the speed of light is an unattainable upper limit for the theory of relativity. Getting to two-thirds of the Nyquist frequency is easy, but getting closer requires more Volts Figure 18.2 Reconstructing the audio wave from samples. 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. Speech Coding Key Data Concepts Volts Figure 18.3 Linear PCM sampling of an audio signal. effort. Close to the Nyquist frequency, very small perturbations in the sample values make large errors in the audio output. Using 8000 samples for 3300 Hz gives the tele- phone system some extra room for sampling inaccuracies that using 7000 samples would not. 2 Now that we have discussed sampling of time, we consider dividing the voltage range into discrete levels, first linear and then logarithmic. Quantization is the term for di- viding continuous measurement into discrete leve