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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