Digital Signal Processing Reference
In-Depth Information
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Figure 2.2
Discrete-time complex exponential
x
[
n
]=
(real and imaginary
parts).
neighbors, giving the illusion of a continuous-time function: while
this makes the plot easier on the eye, it must be remembered that the
signal is defined only over a
discrete
set.
2.1.1
The Discrete-Time Abstraction
While analytical forms of discrete-time signals such as the ones above are
useful to illustrate the key points of signal processing and are absolutely
necessary in the mathematical abstractions which follow, they are non-
etheless just that, abstract examples. How does the notion of a discrete-
time signal relate to the world around us? A discrete-time signal, in fact,
captures our necessarily limited ability to take repeated accurate measure-
ments of a physical quantity. We might be keeping track of the stock market
index at the end of each day to draw a pencil and paper chart; or we might
be measuring the voltage level at the output of a microphone 44,100 times
per second (obviously not by hand!) to record some music via the com-
puter's soundcard. In both cases we need “time to write down the value”
and are therefore forced to neglect everything that happens between mea-
