Representation of Audio Signals 485There are many variations on the use of this technique with one common approach being
to split the conversion into two stages. Typically, a 16-bit converter would have the top 8
most signifi cant bits control a separate conversion stage, which sets either the voltage or
the current with which the lower 8 LSBs operate. The approach has to contend with the
problem of ensuring that the changeover point between the two stages remains matched
throughout the environmental range of the converter. One solution to the problem of
achieving an accurate binary ratio between successive currents is to use a technique called
dynamic element balancing.
Whereas sampling correctly executed loses no information, quantizing inevitably
produces an error. The level of error is essentially dependent on the resolution with which
the quantizing is carried out. Figure 15.26 illustrates the point by showing a sinusoid
quantised to 16 quantizing levels. A comparison of the quantized output with the original
has been used to create the plot of the error in the quantizing. The error waveform of this
example clearly shows a high degree of structure, which is strongly related to the signal
(^10) 50 0 50 100 150 200 250 300
8
6
4
2
0
2
4
6
8
(^010)
0 1 0 1 0 1 0 1 1 1 0 1 0 1 0
0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0
0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0
1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
Time
5 bit 2’s complement
Figure 15.26 : The input sinusoid is shown here prior to sampling as a dotted line
superimposed on the staircase shape of the quantized input signal. The two’s complement
value of the level has been shown on the left-hand edge. The error signal is the difference
between the quantized value and the ideal value assuming a much fi ner resolution. The error
signal, or quantizing noise, lies in the range of l q. Consideration of the mean square error
leads to the expression for the rms value of the quantizing noise: Vqnoise /√()12 where
q is the size of a quantizing level. The maximum rms signal amplitude that can be described
isVqsignal / 22 n^1 √. Together the expression combines to give the expression for
SNR(indB):SNBdB 6.02n 1.76.