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When transporting analog voice long distances, problems with signal loss are often encountered. To counteract this, amplifiers can be used to boost the signal along the path. However, amplifiers amplify both the voice signal and any ambient line noise which may have been picked up on the long circuit. So as the voice signal degrades in magnitude, the ratio of line noise to voice signal increases and the output becomes unacceptable. This problem limits the effectiveness and reach of analog-based long distance connections.

Page 47 transmissions to span greater distances while maintaining acceptable signal loss and

signal-to-noise levels throughout the network. Given the advantages of digital transmission, a method of converting voice signals, which are inherently analog in nature, to a digital format was required.

Pulse code modulation, or PCM, was the solution developed. The concept behind PCM is to sample the audio wavelength at regular intervals and to encode an integer value for its amplitude at each interval. After conversion, the integer values are transmitted over a digital circuit as binary 0s and 1s. The receiving station then uses these integers to reconstruct the waveform and produce an analog signal equivalent to the original analog signal.

One of the factors that affects the quality of PCM voice is the number of wavelength samples taken every second. The more frequent the samples, the more accurately they will portray the shape of the wavelength. Figure 3-13 demonstrates the differences between two sampling rates. The samples are represented by the bars in each graph. Figure 3-13b uses a sampling rate which is twice that of Figure 3-13a. Noticeably, the samples in Figure 3-13b do a better job of

approximating the actual curve than do the bars in a, which miss entire inflections in the waveform. Determining the optimum sampling rate for voice traffic has thus become an important area of research.

Nyquist's theorem states that in order to effectively reconstruct an analog signal, the waveform must be sampled at twice the maximum analog frequency of interest. In other words, to

effectively reconstruct signals of up to 1000 Hz, the waveform must be sampled at 2000 Hz and digitally encoded creating 2000 digital values of the waveform per second. If the values were one byte in magnitude, they would require 16,000 bps (2000 samples / second * 8 bits/byte) to

characterize the signal. Normal voice signals generally fall within the frequency range of 300 and 3400 Hz. In order to transport this frequency range, an upper limit of 4000 Hz was selected. Using Nyquist's theorem, the minimum required sample rate is 8000 Hz. PCM voice therefore samples analog voice at a rate of 8000 times per second. Figure 3-14 shows how a higher sampling frequency will approximate the waveform more effectively.

The second challenge is to encode the waveform at each sample interval. In order to map the amplitude of an analog waveform to digital values, a consistent method of transforming analog values to digital values is required. The greater the range of permitted values, the more accurate a representation can be made. However, using a large range of values requires additional bits. For example, using an 8-bit data field provides 256 different values while a 16-bit data field provides 65,536 different

Figure 3-13

Waveform approximation, showing (a) extremely low sample frequency and(b) twice the frequency of samples in a.

Figure 3-14

More granular waveform sampling.

values for amplitude quantization, but requires twice as much bandwidth to transmit. To limit the amount of data required to store the amplitude, an 8-bit representation was agreed upon by the industry. However, to support a large range of amplitudes without overshadowing lower levels, a logarithmic scale is used to encode amplitude values in the 8-bit field. This allows the 8-bit field to represent amplitude values of 12 to 13 bits in size by effectively compressing the value using the logarithmic scale. The benefit is that the logarithmic scale provides for more granular quantization of low-amplitude signals and coarser quantization of larger amplitude signals. This operation of compressing the amplitude value on encoding and expanding it upon decoding is called com-panding. The logarithmic parameter used for the encoding is sometimes called a compander.

Not surprisingly, two different companders are in use today, resulting in two different coding schemes called mu law and a law. The mu law coding scheme uses a compander which provides slightly better signal-to-noise ratios for low-amplitude signals, while a law uses a compander which provides lower idle channel noise. Mu law is used in the United States and Japan, while a law is used in European networks. The selection of a coding mechanism is usually a

country-wide standard. The mu-law device is responsible for performing any mu-law to a-law conversions when crossing borders.

The above information establishes that PCM uses an 8000-Hz sample rate and that 8-bit amplitude values are generated every interval. This

Page 50 translates to a 64-kbps bandwidth requirement (8000 samples / second * 8 bits / sample = 64,000 bps). Both a-law and mu-law PCM encoding is described in the ITU-T G.711 recommendation.