The complete (continuous) frequency response is defined using the DTFT (see
where the summation limits are truncated to because
is zero for and . Thus, the DTFT can be obtained from
the DFT by simply replacing by , which corresponds
to infinite zero-padding in the time domain. Recall from
§7.2.8 that zero-padding in the time domain gives
ideal interpolation of the frequency-domain samples
(assuming the original DFT included all nonzero samples of ).