Multirate Noble Identities

Multirate Noble Identities

Downsamplers and upsamplers are linear, time-varying operators. Therefore, operation order is very important.

$\begin{psfrags}\psfrag{nd}{ $N\downarrow$\ }\psfrag{hz}{ $H(z)$\ }\psfrag{hzn}{ $H(z^N)$\ }\psfrag{equal}{ $\equiv$\ }\begin{center}\epsfig{file=eps/noble.eps,width=6in} \\ Multirate noble identities \end{center} \end{psfrags}$

It is also important to note that adders or multipliers (any memoryless operators) can commute across downsamplers and upsamplers:

$\epsfig{file=eps/noble_commute.eps,width=6in}$

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``Multirate, Polyphase, and Wavelet Filter Banks'', by Julius O. Smith III, Scott Levine, and Harvey Thornburg, (From Lecture Overheads, Music 421).
Copyright © 2020-06-02 by Julius O. Smith III, Scott Levine, and Harvey Thornburg
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University
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