s that concentrate more on small amplitudes. Employing a logarithmic scale allows quantization intervals to increase with amplitude, and ensures that low-amplitude signals are digitized with smaller quantization error. In other words, fewer bits per sample will be necessary to provide a specified SNR for small signals and an adequate dynamic range for large signals. Companding laws are used to implement logarithmic quantization. A-law and u-law are companding schemes commonly used in telephone networks. While u-law is mainly used in North America and Japan, European countries mostly use A-law. According to u-law, if the normalized input signal is presented by V, the normalized compressed signal, Vc, is defined as sgn(Vi) -1<Vi<1 (1.18) where u is defined as the compression parameter (i.e., a higher value of u results in more compression). The u-law companding is commonly implemented with a value of equal to 255. The transfer function of A-law companding is also given by A.IVil 1+In(A) IVil<1/1 Vc=sgn(Vi)x (1.19) 1+In(A) where A is the compression parameter. In Europe, the E1 lines use A-law companding with A = 87.7, although the value of A = 87.6 is also used. Figure 1.14 shows the transfer function of u-law and A-law companding schemes for different values of u and A. Chapter 1 Voice Transmission A = 20 u=255 A = 87.7 A = 5 Fig. 1.14 Transfer function of (a) u-law companding and (b) A-law companding. There are many similarities between these two schemes. For example, both companding laws are implemented using 8-bit codewords (256 levels, one for each quantization interval). In addition, in both schemes, the whole dynamic range is divided into 16 segments (8 posi- tive and 8 negative) where the length of each segment is twice the length of the proceeding segment. Considering the total 256 quantization levels, this means there are 16 quantization levels inside each segment. These steps are uniformly distributed during each segment. In an 8-bit word, the first 4 bits identify the segment, and the rest quantize the 