represent the analogue signal. Vm = 1/NA (19.49) 19/16 Digital modulation (19.50) can lead to a variation of up to 30dB between one speaker and volts another (Purton, 1962). There is, therefore, a requirement for a wide dynamic range to be coded by the ADC for a speech signal. Therefore, the signal/quantisation noise ratio (SQNR) is as in A uniform quantiser has a constant noise power, independent of Equation 19.51. the signal level. Equation 19.53 shows that to code a signal with a dynamic range of 50dB, maintaining a signal to noise ratio of at least (19.51) 30dB over that dynamic range, would require a 13-bit uniform quantiser. The ear, however, is a very non-linear sensor and, in the presence of a speech signal, any broadband noise which is 30dB quieter than the signal is masked by that speech. So, why use a Expressing this in decibels gives Equation 19.52. uniform quantiser with its fixed noise power, unaffected by speech level? What is really needed is a quantiser which has a constant (19.52) signal to noise ratio of 30dB over a 50dB dynamic range. The signal/quantising noise ratio for small signals could be im- Now, for binary encoded PCM, N = 2k where k is the number of proved by compressing the level range before coding and using bits in the codeword. Substituting in Equation 19.51 gives Equation expansion after decoding at the receiver (i.e. companding). 19.53. It is not necessary to use a 'syllabic' compander, because the process can be performed independently on each speech sample. SQNR = 1.8 + 20klog.,2_d Such an 'instantaneous' compressor could be implemented by a = 1.8 + 6k dB (19.53) non-linear characteristic for which constant increments (8 in out- put voltage correspond to input voltage increments (8) which are Equation 19.53 shows that adding one digit to the code improves the SQNR by 6dB. Since the quantisation noise level is independent proportional to the input voltage X, as shown in Figure 19.19(b). of signal level, a signal whose level is xdB lower than the maximum Thus Equations 19.54 and