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4.9 Polyphase decimation filter

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Implementation of polyphase decimation filters.

Polyphase decimation

Recall the standard decimation method in [link] .

Note that this procedure is computationally inefficient because it discards the majority of the computed filteroutputs. Through the use of the Noble identities, it is possible to rearrange [link] so that filter outputs are not discarded.

In order to apply the Noble identity for decimation, we must transform H z into its upsampled polyphase components H p z M , p 0 … M 1 , defined previously in the context of polyphase interpolation .

H z n n h n z n k k p 0 M 1 h k M p z k M p
via ≔ k n M , ≔ p n M
H z p 0 M 1 k k h p k z k M z p
via ≔ h p k h k M p
H z p 0 M 1 H p z M z p
Using these unsampled polyphase components, the preceding block diagram can be redrawn as [link] .

Applying the Noble identity for decimation to [link] yields [link] . The ladder of delays and downsamplers on the left below accomplishes a form ofserial-to-parallel conversion.
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Source:  OpenStax, Fundamentals of signal processing. OpenStax CNX. Nov 26, 2012 Download for free at http://cnx.org/content/col10360/1.4
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