## Pulse Coded Modulation PCM

Before going any further into the DS-1, it may be appropriate to review the modulation technique used to create the digital signal. When DS-1 was first created, it was designed around converting analog voice communications into digital voice communications. To do that, voice characteristics were analyzed. What the developers learned was that voice operates in a telephony world in a band-limited channel operation. The normal voice will produce both amplitude and a frequency change ranging from 100 to approximately 5,000 times a second. These amplitude and frequency shifts address normal voices. However, the telephone companies decided long ago that carrying true voice would be too expensive and would not provide any real added value to the conversation. They then determined that the normal conversation from a human actually carries the bulk of the information when the frequency and amplitude shifts vary between 100 and 3,300 times per second. Armed with this information, the developer determined that reasonable and understandable voice could be handled when carried across a band-limited channel operating at 3,000 cycles of information per second (what was termed as a 3 kHz channel). Taking all the electromagnetic spectrum available to them, the developers then channelized the frequency spectrum (in radio frequencies [RF] and in electrical spectrum available on the cabling systems they had) to smaller capacities. The norm was set at 4 kHz channels. This is the foundation of the voice telephone network.

From there, the providers of the infrastructure (the telephone companies) placed bandpass filters on the facilities to limit the amount of electrical information that could pass across their wires (or any other communications facility). Using a standard 4 kHz channel, they limited the bandpass to no more than 3 kHz (see Figure 28-3).

4 kHz

4 kHz

### 300 3300

Figure 28-3: Band-limited channel limits the amount of information carried to 3 kHz. Following up on this thought, the developers then wanted to convert the analog communications to a digital format. Here they studied the way the user modulates voice conversation. Now they had something to work with. The voice modulated at a normal rate operates in the 3 kHz range but now must be converted to a digital signal consisting of 1s and 0s. Using the Nyquist theorem from 1934, the developers used a formula to convert the continuously changing amplitude and frequency shifts to a discreet set of values represented by the 1s and 0s. Using a three-step process, as shown in Table 28-1, they determined that they could carry digital voice. The table represents the three steps followed to do this conversion.

 Process Result 1. Sample the analog wave at twice the highest range of frequencies that can be carried across the line. Using a 4 kHz channel capacity, the highest range of frequencies allowable is 4,000. A sampling rate of 8,000 times per second: 4,000 x 2 = 8,000. 2. Quantify the values using a logical pattern of 1s and 0s to represent the height of the signal at any point in time. This deals with the amplitude shifts only. Using an 8-bit sequence, the result is a total of 256 combinations of amplitude that can be represented. Although there may be more amplitude heights (values), the 256 quantities were determined to be sufficient. 2 = 256 possible combinations. 3. After the values are determined from the samples, the final step is to encode the signal into a digital format and transmit information in its digital format onto the wires. A sample value of 5 on the positive side of the wave will then be represented as an 8-bit data stream. Binary 5 = 00000101.

Once the values were determined, the developers used another process. Setting the values in place, they had to determine where along the wave the sample fell. They created a value system to show the 256 levels by using the table shown in Table 28-2. First, the digital PCM signal is representative of both positive and negative values. To reflect where along the wave the sample fell, the eighth bit in each sample is used as a sign (+/-) value. The other seven bits, therefore, represent the actual sample value. There are 128 points on the positive side of the wave and 128 points on the negative side of the wave. In this table, we look at the major stepping points. Two different formats are shown in the table, the PCM used in North America (and Japan) is M^Law, whereas the rest of the world uses an A-Law method. These are different as shown.

Table 28-2: Summary of values for PCM in Mu-law and A-Law formats

 Coded Numerical Value Bit Number Comments Mu-Law A-Law The left-most bit (bit 12345678 12345678 number 1) is transmitted +127 10000000 11111111 first. It is the most + 96 10011111 11100000 significant bit. This bit is + 64 10111111 11000000 used as the sign bit; it is a + 32 11011111 10100000 1 for positive values, and it 0 11111111 10000000 is a 0 for negative values. 0 01111111 00000000 -32 01011111 00100000 Note that 0 has two -64 00111111 01000000 different values. Bits 2 to 8 -96 00011111 01100000 are inverted between -126 00000001 01111110 A-Law PCM and Mu-Law -127 00000000 01111111 PCM. In A-Law, all even bits are inverted prior to transmission.

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