Digital Signal Processing Reference
In-Depth Information
l
g
r
,
y
i
d
.
,
©
,
L
s
Chapter 11
Multirate Signal Processing
The sampling theorem in Chapter 9 provided us with a tool tomap a contin-
uous-time signal to a sequence of discrete-time samples taken at a given
sampling rate. By choosing a different sampling rate, the same continuous-
time signal can bemapped to an arbitrary number of different discrete-time
signals. What is the relationship between these different discrete-time se-
quences? Can they be transformed into each other entirely from within the
discrete-time world? These are the questions that multirate theory sets out
to answer.
The conversion from one sampling rate to another can always take the
“obvious” route via continuous time, i.e. via interpolation and resampling.
This is clearly disadvantageous, both from the point of view of the needed
equipment and from the point of view of the quality loss which always takes
place upon quitting the digital discrete-time domain. That was the ratio-
nale, for instance, of an infamous engineering decision taken by the audio
industry in the early 90's. In those years, after compact disk players had
been around for about a decade, digital cassette players started to appear
in the market under the name of DAT. The decision was to use a different
and highly incompatible sampling rate for the DAT with respect to the CD
(48Khzvs.44.1Khz)soastomakeitdifficulttoobtainperfectdigitalcopies
of existing CDs.
(1)
Multirate signal processing rendered that strategy moot,
as we will see.
More generally, multirate signal processing not only comes to helpwhen-
ever a conversion between different standards is needed, but it is also a full-
fledged signal processing tool in its own right with many fruitful applica-
tions in the design of efficient filtering schemes and of telecommunication
(1)
While DATs are all but extinct today, the problem remains of actuality since DVDs sport
a sampling rate of 48 Khz as well.
