dB5K 10K 20K Fs 2 Fs 3 Fs
Frequency H 3
(a)Figure 15.21 : (a) The frequency domain view of the sampling operation requires us to
recognize that the spectrum of a perfectly shaped sampling pulse continues forever. In
practice sampling, waveforms do have fi nite width and practical systems do have limited
bandwidth. We show here the typical spectrum of a musical signal and the repeated
spectrum of the sampling pulse using an extended frequency axis. Note that even modern
musical signals do not contain signifi cant energy at high frequencies and, for example, it
is exceedingly rare to fi nd components in the 10-kHz region more than 30 dB below the
peak level. (b) The act of sampling can also be appreciated as a modulation process, as the
incoming audio signal is being multiplied by the sampling waveform. The modulation will
develop sidebands, which are refl ected on either side of the carrier frequency (the sampling
waveform), with a set of sidebands for each harmonic of the sampling frequency. The
example shows the consequence of sampling an audio bandwidth signal that has frequency
components beyond F 2 /2, causing a small but potentially signifi cant amount of the fi rst
lower sideband of the sampling frequency to be folded or aliased into the intended audio
bandwidth. The resulting distortion is not harmonically related to the originating signal and
can sound truly horrid. Use of an antialias fi lter before sampling restricts the leakage of the
sideband into the audio signal band. The requirement is ideally for a fi lter with an impossibly
sharp rate of cutoff, and in practice a small guard band is allowed for tolerance and fi nite
cutoff rates. Realizing that the level of audio signal with a frequency around 20 kHz is
typically 60 dB below the peak signal level, it is possible to perform practical fi ltering
using seventh-order fi lters. However, even these fi lters are expensive to manufacture
and represent a signifi cant design problem in their own right.
dB22 kH 3 44 kH 3 88 kH 3
Frequency H 3
(b)Filter response