### Interpolation Operator

The *interpolation operator*
interpolates a signal
by an integer factor using bandlimited interpolation. For
frequency-domain signals
,
, we may
write spectral interpolation as follows:

Since
is initially only defined over
the roots of unity in the plane, while
is defined
over roots of unity, we define
for
by
ideal bandlimited interpolation (specifically *time*-limited
spectral interpolation in this case).

For time-domain signals , exact interpolation is similarly bandlimited interpolation, as derived in Appendix D.

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Repeat Operator

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Ideal Spectral Interpolation