le- ment the compander. By increasing the amount of compression, we increase the dynamic range at the expense of the S/N for high signal amplitudes. One family of compression characteristics (Recommendation G.733) used in North America and Japan is the u-law companding, which is defined as follows: (3.8) where X is the signal value, Z(x) represents the compressed signal, sgn(x) is the polarity (+ or -) of X and is the constant with a standard value of 255. Another approach is A-law companding (Recommendation G.732) used as a European standard, where the curve is divided into linear and loga- rithmic sections: (3.9) Ax for Signals Carried over the Network where X is the signal value, Z(x) represents the compressed signal, sgn(x) is the polarity (sign) of X, and A is a constant with a standard value of 87.6. In the case of A-law companding, the SQR is constant in the logarith- mic section and directly proportional to the signal value in the linear section; see the dashed line in Figure 3.13. ITU-T/CCITT recommendations define the continuous curves given by the preceding formulas but approximate them with a curve with linear segments for easier implementation. As an example of the performance of a nonlinear coding scheme, Figure 3.13 represents the SQR dependence on the signal level for A-law companding. The signal level is measured in dBm0, which we explain at the end of this chapter and may vary within the range of 40 dB while SQR remains nearly unchanged. However, when signal level is high, linear quan- tizing would give better performance, as the "without companding" dashed line shows. We see from Figure 3.13 that at low levels the SQR of A-law compand- ing is more than 20 dB better than linear coding. The curve gives this per- formance when the signal is a sine wave and the ripple of the curve is a consequence of the approximation of the compression curve with linear segments. 3.6.6 Binary Coding Finally, in the PCM encoding process each sample is represented as one in the set of eight-bit binary words. As an e