Audio Engineering

498 Chapter 16

Input waveform

Time

Digitised ‘staircase’

waveform

Permissible step levels

Figure 16.1 : Digitally encoded/decoded waveform.

Error magnitude Time

Figure 16.2 : Quantization error.

signals. I will consider this defect, and the ways by which it can be minimized, later in
this chapter.

16.1.2 Bandwidth

The second practical problem is that of the bandwidth necessary to store or transmit
such a digitally encoded signal. In the case of the CD, the specifi ed audio bandwidth is
20 Hz to 20 kHz, which requires a sampling frequency somewhat greater than 40 kHz.
In practice, a sampling frequency of 44.1 kHz is used. In order to reduce the extent of
the staircase waveform quantization error, a 16-bit sampling resolution is used in the
recording of the CD, equivalent to 216 or 65,536 possible voltage steps. If 16 bits are to
be transmitted in each sampling interval, then, for a stereo signal, the required bandwidth
will be 2 × 16 × 44100 Hz, or 1.4112 mHz, which is already 70 times greater than the