500 Chapter 16
fs is the sampling frequency and fm is the upper modulation frequency. Because of the
way in which the sampling process operates, it is not possible to distinguish between a
signal having a frequency that is somewhat lower than half the sampling frequency and
one that is the same distance above it; a problem called “ aliasing. ” In order to avoid this,
it is essential to limit the bandwidth of the incoming signal to ensure that it contains no
components above fs /2.
If, as is the case with the CD, the sampling frequency is 44.1 kHz and the required audio
bandwidth is 20 Hz to 20 kHz, 0/1 dB, an input “ antialiasing ” fi lter must be employed
to avoid this problem. This fi lter must allow a signal magnitude that is close to 100% at
20 kHz, but nearly zero (in practice, usually 60 dB) at frequencies above 22.05 kHz.
It is possible to design a steep-cut, low-pass fi lter that approximates closely to this
characteristic using standard linear circuit techniques, but the phase shift and group delay
(the extent to which signals falling within the affected band will be delayed with respect
of lower frequency signals) introduced by this fi lter would be too large for good audio
quality or stereo image presentation.
Figure 16.3 : PCM frequency spectrum (a) when sampled at 44.1 kHz and (b) when four
times oversampled.0 22.05 kHz 44.1 kHz 88.2 kHz 132.3 kHz 176.4 kHzFrequencyfmfsetc.Output(a)0 22.05 kHz 44.1 kHz 88.2 kHz 132.3 kHz 176.4 kHzFrequencyfmfsOutput(b)