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192 CHAPTER EIGHT
Inputs
Anti-alias
Converter
Converter
Engine
Filter A/D DSP D/A Outputs
FIGURE 8-1 A block diagram of a typical DSP computer
them periodically with the A/D, and it has no idea what the signals do between samples.
We’ll state the main theorem used in DSP and then demonstrate that we already know
the theorem and use it instinctively every day.

The Nyquist-Shannon

Sampling Theorem

We cannot capture the essence of a digitized signal without sampling it at a frequency
twice that of the signal. Stated another way, we must sample a signal twice as fast as the
highest-frequency component in the signal.

ANTI-ALIASING FILTER

To successfully sample a signal, we must first alter it to filter out all the frequency com-
ponents that are above half the sampling frequency. The frequency at 50 percent of the
sampling frequency is also called the Nyquist Frequency. We’ll get into a discussion
about just what aliasing means later. These statements are oversimplifications of the
original theorem. Consult the URLs near the end of this section for a more thorough
treatment.
So where do we use all this math theory in our daily lives? Here’s one for readers with
kids. Nobody pays constant attention to the kids. It’s impossible to do so because it takes
too much energy and, further, paying constant attention teaches them nothing. Instead,
we sample their behavior periodically by listening in on them. Often we turn our heads,
cup our ears to listen, and say, “Gee, it’s way too quiet up there.” Oddly enough, with
kids, the total lack of input is the very signal that something is wrong.
That was an easy example. Here’s a harder one. Consider the following experiment
—don’t do it for real. While you are a passenger, just imagine you are driving and pay-
ing attention to the road. Drive down the street past a long row of parked cars. At a con-
stant speed, pass one parked car each second. It’s not possible to watch every car every
second. The truth is, we sample the road ahead with our eyes.