Stretch Operator
Unlike all previous operators, the
operator maps
a length
signal to a length
signal, where
and
are integers.
We use ``
'' instead of ``
'' as the time index to underscore this fact.
A stretch by factor is defined by
![$\displaystyle \hbox{\sc Stretch}_{L,m}(x) \isdef
\left\{\begin{array}{ll}
x(...
...x{ an integer} \\ [5pt]
0, & m/L\mbox{ non-integer.} \\
\end{array} \right.
$](http://www.dsprelated.com/josimages_new/mdft/img1217.png)


![$\displaystyle \hbox{\sc Stretch}_3([4,1,2]) = [4,0,0,1,0,0,2,0,0].
$](http://www.dsprelated.com/josimages_new/mdft/img1219.png)
The stretch operator is used to describe and analyze upsampling,
that is, increasing the sampling rate by an integer factor.
A stretch by followed by lowpass filtering to the frequency band
implements ideal bandlimited interpolation
(introduced in Appendix D).
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