 say let's just throw away the remainders. That which we throw away is the error between the quantized value and the real value. That which we throw away gives rise to quantization distortion. In Figure 6.3, maintaining the -1, 0, +1 V relationship, let us double the number of quantum steps from 16 to 32. What improvement would we achieve in quantization distortion? First determine the step increment in millivolts in each case. In the first case the total range of 2000 mV would be divided into 16 steps, or 125 mV/step. The second case would have 2000/32 or 62.5 mV/step. For the 16-step case, the worst quantizing error (distortion) would occur when an input to be quantized was at the half-step level or, in this case, 125/2 or 62.5 mV above or below the nearest quantizing step. For the 32-step case, the worst quantizing error (distortion) would again be at the half-step level, or 62.5/2 or 31.25 mV. Thus the improvement in decibels for doubling the number of quantizing steps is 20 log log 2 or 6 dB (approximately). 31.25 This is valid for linear quantization only. Thus increasing the number of quantizing steps for a fixed range of input values reduces quantizing distortion accordingly. Voice transmission presents a problem. It has a wide dynamic range, on the order of 50 dB. That is the level range from the loudest syllable of the loudest talker to lowest- level syllable of the quietest talker. Using linear quantization, we find it would require 2048 discrete steps to provide any fidelity at all. Since 2048 is 211. this means we would need an 11-bit code. Such a code sampled 8000 times per second leads to 88,000-bps 6.2 BASIS OF PULSE CODE MODULATION equivalent voice channel and an 88-kHz bandwidth, assuming 1 bit per Hz. Designers felt this was too great a bit rate/bandwidth. They turned to an old analog technique of companding. Companding derives from two words: compression and expansion. Compression takes place on the transmit side of the circuit, while expansion occurs on the receive side. Compression reduces t