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Figure 3-67 PAM samples
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Figure 3-68 Quantizing the samples
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discern the shape of the original wave from their collective amplitudes. Imagine also that we have graphed these samples in such a way that the wave of sample points meanders above and below an established zero point on the x-axis, so that some of the samples have positive values and others are negative, as shown. The amplitude levels allow us to assign values to each of the PAM samples, although a glaring problem with this technique should be obvious to the careful reader. Very few of the samples actually line up
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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.
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exactly with the amplitudes delineated by the graphing process. In fact, most of them fall between the values, as shown in the illustration. It doesn t take much of an intuitive leap to see that several of the samples will be assigned the same digital value by the coder-decoder that performs this function, yet they are clearly not the same amplitude. This inaccuracy in the measurement method results in a problem known as quantizing noise, and is inevitable when linear measurement systems, such as the one suggested by the drawing, are employed in coder-decoders (CODECs). Needless to say, design engineers recognized this problem rather quickly, and equally quickly came up with an adequate solution. It is a fairly well-known fact among psycholinguists and speech therapists that the human ear is far more sensitive to discrete changes in amplitude at low-volume levels than it is at high-volume levels, a fact not missed by the network designers tasked with optimizing the performance of digital carrier systems intended for voice transport. Instead of using a linear scale for digitally encoding the PAM samples, they designed and employed a nonlinear scale that is weighted with much more granularity at low volume levels that is, close to the zero line than at the higher amplitude levels. In other words, the values are extremely close together near the x-axis and get farther and farther apart as they travel up and down the y-axis. This nonlinear approach keeps the quantizing noise to a minimum at the low-amplitude levels where hearing sensitivity is the highest, and allows it to creep up at the higher amplitudes, where the human ear is less sensitive to its presence. It turns out that this is not a problem, because the inherent shortcomings of the mechanical equipment (microphones, speakers, the circuit itself) introduce slight distortions at high-amplitude levels that hide the effect of the nonlinear quantizing scale. This technique of compressing the values of the PAM samples to make them fit the nonlinear quantizing scale results in a bandwidth savings of more than 30 percent. In fact, the actual process is called companding, because the sample is first compressed for transmission, then expanded for reception at the far end, hence the term. The actual graph scale is divided into 255 distinct values above and below the zero line. In North America and Japan, the encoding scheme is known as m-Law (Mu-Law); the rest of the world relies on a slightly different standard known as A-Law. There are eight segments above the line and eight below (one of which is the shared zero point); each segment, in turn, is subdivided into 16 steps. A bit of binary mathematics now allows us to convert the quantized amplitude samples into an eight-bit value for transmission. For the sake of demonstration, let s consider a negative sample that falls into the
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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.
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