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:
![\begin{eqnarray*}
\hbox{\sc Interp}_{L,k^\prime }(X) &\isdef & X(\omega_{k^\prim...
...i k^\prime /M,\; k^\prime =0,1,2,\dots,M-1,\;\\
M&\isdef & LN.
\end{eqnarray*}](http://www.dsprelated.com/josimages_new/mdft/img1247.png)
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