Multirate Noble Identities
Figure 11.13 illustrates the so-called noble identities for
commuting downsamplers/upsamplers with ``sparse transfer functions''
that can be expressed a function of 
. Note that downsamplers
and upsamplers are linear, time-varying operators. Therefore,
operation order is important. Also note that adders and multipliers
(any memoryless operators) may be commuted across downsamplers and
upsamplers, as shown in Fig.11.14.
![\begin{psfrags}
% latex2html id marker 29805\psfrag{nd}{ $N\downarrow$\ }\psfrag{hz}{ $H(z)$\ }\psfrag{hzn}{ $H(z^N)$\ }\psfrag{equal}{ $\equiv$\ }\begin{figure}[htbp]
\includegraphics[width=0.9\twidth]{eps/noble}
\caption{Multirate noble identities}
\end{figure} % was 6in
\end{psfrags}](http://www.dsprelated.com/josimages_new/sasp2/img1979.png)
![\includegraphics[width=0.9\twidth]{eps/noble_commute}](http://www.dsprelated.com/josimages_new/sasp2/img1980.png)
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Filtering and Downsampling, Revisited
