1
$\begingroup$

Polyphase implementations of upsampling/ interpolation and downsampling/ decimation, after having invoked the Noble identities, are presented as follows (taken from Proakis):

Three Channel Polyphase Decimation (Three-Channel Polyphase Decimation) Three Channel Polyphase Interpolation (Three-Channel Polyphase Interpolation)

The decimation always seems to use the direct form (delay before filtering), while the interpolation always seems to use the transposed form (delay after filtering). I understand that these two forms are equivalent (or believe that's the case). But I'm unable to find an explicit discussion on why this is canonical; why, for instance, doesn't the interpolation use the direct form? I've seen a couple of suggestions that it has something to do with the critical path, but I'm not clear on precisely what this means.

Could anyone clear this up? I suspect I'm being a bit obtuse...

Improve this question
$\endgroup$

1 Answer 1

Reset to default
1
$\begingroup$

The antialiasing filters here are FIR so there's no difference in the order of operations. If they were IIR there would be implications, see NUMERICAL ROBUSTNESS OF TDF-II. I think the classical representation of polyphase decimators and interpolators here is an elegant way to say that filtering has to occur at the lowest rate (before interpolation or after decimation).

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.