Digital Signal Processing Reference
In-Depth Information
more importantly,
cheap
designs introduce imprecisions in the final result
(good slide rules used to be
very
expensive). On the other hand the aba-
cus, working only with integer arithmetic, is a perfectly precise machine
(5)
even if it's made with rocks and sticks. Digital signal processing works with
countable sequences of integers so that in a digital architecture no process-
ing noise is introduced. A classic example is the problem of
reproducing
a
signal. Before mp3 existed and file sharing became the bootlegging method
of choice, people would “make tapes”. When someone bought a vinyl record
he would allow his friends to record it on a cassette; however, a “peer-to-
peer” dissemination of illegally taped music never really took off because of
the “second generation noise”, i.e. because of the ever increasing hiss that
would appear in a tape made from another tape. Basically only first genera-
tion copies of the purchased vinyl were acceptable quality on home equip-
ment. With digital formats, on the other hand, duplication is really equiva-
lent to copying down a (very long) list of integers and even very cheap equip-
ment can do that without error.
Finally, a short remark on terminology. The amplitude accuracy of a set
of samples is entirely dependent on the processing hardware; in current
parlance this is indicated by the number of
bits per sample
of a given rep-
resentation: compact disks, for instance, use 16 bits per sample while DVDs
use 24. Because of its “contingent” nature, quantization is almost always ig-
nored in the core theory of signal processing and all derivations are carried
out as if the samples were real numbers; therefore, in order to be precise,
we will almost always use the term
discrete-time
signal processing and leave
the label “digital signal processing” (DSP) to the world of actual devices. Ne-
glecting quantization will allow us to obtain very general results but care
must be exercised: in the practice, actual implementations will have to deal
with the effects of finite precision, sometimes with very disruptive conse-
quences.
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1.4
Communication Systems
Signals in digital form provide us with a very convenient abstract represen-
tation which is both simple and powerful; yet this does not shield us from
the need to deal with an “outside” world which is probably best modeled by
the analog paradigm. Consider a mundane act such as placing a call on a
cell phone, as in Figure 1.9: humans are analog devices after all and they
produce analog sound waves; the phone converts these into digital format,
(5)
As long as we don't need to compute square roots; luckily,
linear
systems (which is what
interests us) are made up only of sums and multiplications.
