Filtering and Downsampling, Revisited
Let's return to the example of §11.1.3, but this time have the FIR lowpass filter h(n) be length , . In this case, the polyphase filters, , are each length .12.2 Recall that
(12.15) |
leading to the result shown in Fig.11.11.
Next, we commute the : downsampler through the adders and upsampled (stretched) polyphase filters to obtain Fig.11.12. Commuting the downsampler through the subphase filters to obtain is an example of a multirate noble identity.
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Multirate Noble Identities
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Type II Polyphase Decomposition