Polyphase Resampling 2.8 2002/01/09 2003/01/15 Phil Schniter schniter@ee.eng.ohio-state.edu Adan Galvan jago@rice.edu Erin Maloney emaloney@rice.edu Phil Schniter schniter@ee.eng.ohio-state.edu CD compact disc DAT digital audio tape polyphase resampling sample-rate conversion Introduction to the concept of Polyphase Resampling.

Polyphase Resampling with a Rational Factor Recall that resampling by rational rate LM can be accomplished through the following three-stage process(see ).

If we implemented the upsampler/LPF pair with a polyphase filterbank, we would still waste computations due to eventual downsampling by M. Alternatively, if we implemented the LPF/downsampler pair with a polyphase filterbank, we would waste computations by feeding it the (mostly-zeros) upsampler output. Thus, we need to examine this problem in more detail. Assume for the moment that we implemented the upsampler/LPF pair with a polyphase filterbank, giving the architecture in .

Keeping the "parallel-to-serial" interpretation of the upsampler/delay ladder in mind, the input sequence to the decimator ql has the form as in

leading to the observation that q l v l L l L y m q m M v m M L m M L k k h m M L k x m M L k Thus, to calculate the resampled output at output index m, we should calculate only the output of branch number m M L at input index m ML. No other branch outputs are calculated, so that no computations are wasted. The resulting structure is depicted in .

An equally-efficient structure could be obtained if we implemented the LPF/downsampler using the M-branch polyphase decimator which was fed with the proper sequence of input samples. However, this structure is not as elegant: rather than computing the output of one particular polyphase branch per output sample, we would need to add all branch outputs, but where each branch output was calculated using a particular subset of polyphase taps.