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 .