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
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.