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Beginnings
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Pulse Code Modulation (PCM)
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Thanks to work performed by Harry Nyquist at Bell Laboratories in the 1920s, we know that to optimally represent an analog signal as a digitally encoded bitstream, the analog signal must be sampled at a rate that is equal to twice the bandwidth of the channel over which the signal is to be transmitted. Because each analog voice channel is allocated 4 KHz of bandwidth, it follows that each voice signal must be sampled at twice that rate, or 8,000 samples per second. In fact, that is precisely what happens in TCarrier systems, which we will use to illustrate our example. The standard T-Carrier multiplexer accepts inputs from 24 analog channels, as shown in Figure 1-18. Each channel is sampled in turn, every one eight-thousandth of a second in round-robin fashion, resulting in the generation of 8,000 pulse amplitude samples from each channel every second. The sampling rate is important. If the sampling rate is too high, too much information is transmitted and bandwidth is wasted; if the sampling rate is too low, then we run the risk of aliasing. Aliasing is the interpretation of the sample points as a false waveform, due to the paucity of samples. This Pulse Amplitude Modulation process represents the first stage of Pulse Code Modulation, the process by which an analog baseband signal is converted to a digital signal for transmission across the T-Carrier network. Figure 1-19 shows this first step. The second stage of PCM, shown in Figure 1-20, is called quantization. In quantization, we assign values to each sample within a constrained range.
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Figure 1-18 Time division multiplexing.
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Figure 1-19 Pulse Amplitude Modulation (PAM).
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1
Figure 1-20 Quantization and Pulse Code Modulation (PCM).
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Beginnings
Beginnings
For illustration purposes, imagine what we now have before us. We have replaced the continuous analog waveform of the signal with a series of amplitude samples that are close enough together that we can 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. The amplitude levels enable 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 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 came up with an adequate solution just as quickly. It is a fairly wellknown 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 become 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 enables 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 bandwidth savings of more than 30 percent. The actual process is called companding because the sample is first compressed for transmission, then expanded for reception at the far end.
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