Periodic Interpolation (Spectral Zero Padding)

The *dual* of the zero-padding theorem states formally that
*zero padding in the frequency domain* corresponds to *periodic
interpolation* in the time domain:

**Definition: **For all
and any integer
,

where zero padding is defined in §7.2.7 and illustrated in Figure 7.7. In other words, zero-padding a DFT by the factor in the frequency domain (by inserting zeros at bin number corresponding to the

Periodic interpolation is ideal for signals that are *periodic*
in
samples, where
is the DFT length. For non-periodic
signals, which is almost always the case in practice, bandlimited
interpolation should be used instead (Appendix D).

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