| 2.1.1 Sampling at Twice the Maximum Frequency
The general theorem for sampling a bandlimited analog signal (a signal having no frequency
components above a certain frequency f
max
) requires that the sampling rate be at least two times
the highest frequency component of the analog signal 2f
max
. This ensures that the original signal
can be reconstructed exactly from the samples. Figure 1(b) shows an example of sampling a
bandlimited signal with a maximum frequency of f
max
at f
s
=2f
max
. Note that the copies of F(f) that
are present in F
s
(f) do not overlap. As the sampling rate is increased beyond 2f
max
, the copies of
F(f) that are present in F
s
(f) are spread even farther apart. This is shown in Figure 1(c). Sampling
a bandlimited signal at rates equal to or greater than 2f
max
guarantees that spectrum overlap (often
called aliasing) does not occur and that the original analog signal can be reconstructed exactly
[3],[4]. Figure 1(d) shows the spectrum overlap that occurs when sampling at rates less than
2f
max
.
4
Figure 1. Spectrum of: (a) a bandlimited continuous-time analog signal; (b) the signal sampled at
f
s
= 2f
max
; (c) the signal sampled at f
s
> 2f
max
; and (d) the signal sampled at f
s
< 2 f
max
.
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