Digital Signal Processing Reference
In-Depth Information
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Figure 1.1
Temperature measurements over a month.
in one's head, is the earliest and most fundamental form of abstraction; as
children we quickly learn that counting does indeed bring disparate objects
(the proverbial “apples and oranges”) into a common modeling paradigm,
i.e. their cardinality. Digital signal processing is a flavor of signal processing
in which everything
including time
is described in terms of integer num-
bers; in other words, the abstract representation of choice is a one-size-fit-
all countability. Note that our earlier “thought experiment” about ambient
temperature fits this paradigm very naturally: the measuring instants form
a countable set (the days in a month) and so do the measures themselves
(imagine a finite number of ticks on the thermometer's scale). In digital
signal processing the underlying abstract representation is always the set
of natural numbers regardless of the signal's origins; as a consequence, the
physical nature of the processing device will also always remain the same,
that is, a general digital (micro)processor. The extraordinary power and suc-
cess of digital signal processing derives from the inherent universality of its
associated “world view”.
1.1
Some History and Philosophy
1.1.1
Digital Signal Processing under the Pyramids
Probably the earliest recorded example of digital signal processing dates
back to the 25th century BC. At the time, Egypt was a powerful kingdom
reaching over a thousand kilometers south of the Nile's delta. For all its
latitude, the kingdom's populated area did not extend for more than a few
kilometers on either side of the Nile; indeed, the only inhabitable areas in
an otherwise desert expanse were the river banks, which were made fertile
