Sampling Theory
The dual of the Poisson Summation Formula is the continuous-time
aliasing theorem, which lies at the foundation of elementary
sampling theory [264, Appendix G]. If
denotes a
continuous-time signal, its sampled version
,
, is
associated with the continuous-time signal
![]() |
(B.60) |
where



where
denotes the sampling rate
in radians per second. Note that
is periodic
with period
. We see that if
is bandlimited to
less than
radians per second, i.e., if
for all
, then only the
term will be
nonzero in the summation over
, and this means there is no
aliasing. The terms
for
are all
aliasing terms.
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Poisson Summation Formula