Aliasing of Sampled Signals

This section quantifies aliasing in the general case. This result is then used in the proof of the sampling theorem in the next section.

It is well known that when a continuous-time signal contains energy at
a frequency higher than half the sampling rate
, sampling
at
samples per second causes that energy to *alias* to a
lower frequency. If we write the original frequency as
, then the new aliased frequency is
,
for
. This phenomenon is also called ``folding'',
since
is a ``mirror image'' of
about
. As we will
see, however, this is not a complete description of aliasing, as it
only applies to real signals. For general (complex) signals, it is
better to regard the aliasing due to sampling as a summation over all
spectral ``blocks'' of width
.

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