Poisson Summation Formula

As shown in §B.14 above, the Fourier transform of an impulse train is an impulse train with inversely proportional spacing:

(B.56) |

where

(B.57) |

Using this Fourier theorem, we can derive the continuous-time PSF using the

(B.58) |

Using linearity and the shift theorem for

We have therefore shown

Compare this result to Eq. (8.30). The left-hand side of (B.60) can be interpreted ,

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