Editing Poisson summation formula (section)

===Convolution theorem===
{{see also|Convolution theorem#Convolution theorem for tempered distributions}}
The Poisson summation formula is a particular case of the [[convolution theorem]] on [[Distribution (mathematics)#Tempered distribution|tempered distributions]]. If one of the two factors is the [[Dirac comb]], one obtains [[periodic summation]] on one side and [[Sampling (signal processing)|sampling]] on the other side of the equation. Applied to the [[Dirac delta function]] and its [[Fourier transform]], the function that is constantly 1, this yields the [[Dirac_comb#Dirac-comb identity|Dirac comb identity]].