Data Communications Networking Devices - 4th Ed.pdf

654 _________________________ WIDE AREA NETWORK DATA CONCENTRATION EQUIPMENTplotted from the formulaY ˆ AX 0 v V 1 ‡ log AA1 ‡ log …AX† VY ˆ1 ‡ log A A v Vwhere A = 87.6.The curve for the m law can be plotted from the following formula:Y ˆlog …1 ‡ mX†log …1 ‡ m†where m had a value of 100 for the original North American T1 system employingPCM while latter systems use a value of 255. For the preceding formulas:X ˆ vV and Y ˆ iBwhere v represents the instantaneous input voltage, V is the maximum inputvoltage, i is the number of the quantization step, and B is the number of quantizationsteps on each side of the center of the range.CodingThe third step in the PCM process is coding. This process is very closely related toquantization since it must convert the interval in which a sample falls into a binaryvalue. In both North American and European systems eight bits are used to identifythe quantization interval into which a sample falls, resulting in the data rate of PCMbecoming 8000 samples/second X 8 bits/sample, or 64 kbps. However, the actualencoding method differs between each system.In North America PCM systems subdivide the sample interval into 15 non-linearsegments called chords actually 16 since segments cutting the origin are co-linearand are counted as one) with 16 linear intervals per segment that are referred to assteps. Since the code level for 256 quantization values goes from 0 to 255 torepresent a range from peaknegative to peakpositive, four bits are used to denotethe chord and four bits the step in a chord. In comparison, European PCM uses a13-segment approximation of the A-law curve which goes from negative to positive.In the coding method developed for A-law quantization, the ®rst bit indicateswhether the quantization interval is above 1) or below 0) the origin. The followingthree bits identify the chord while the next four bits identify the step in the chord.DS1 framingIn the United States, AT&T originally developed a 24-channel PCM systemknown as DS1, which resulted in the multiplexing of 24 voice conversations onto