pole zero map of DFT

[vishnu36]

single bin DFT can be considered as a filter. How to represent DFT as a pole zero map. Also how do we evaluate frequency response analytically?

 

[FvM]

DFT is normally performed discontinuously. To make filter for continuous signal, you want a continuously running alorithm.

A possible solution is the Goertzel algorithm https://en.wikipedia.org/wiki/Goertzel_algorithm