Computational Savings of Polyphase Resampling 2.0 2003/01/15 2003/01/15 Phil Schniter schniter@ee.eng.ohio-state.edu Adan Galvan jago@rice.edu polyphase resampling

Computational Savings of Polyphase Resampling Recall the standard (non-polyphase) resampler in .

For simplicity, assume that LM . Since the length of an FIR filter is inversely proportional to the transition bandwidth (recalling Kaiser's formula), and the transition bandwidth is directionally proportional to the cutoff frequency, we model the lowpass filter length as N αL, where α is a constant that determines the filter's (and thus the resampler's) performance (independent of L and M). To compute one output point, we require M filter outputs, each requiring NαL multiplies, giving a total of αLM multiplies per output. In the polyphase implementation, calculation of one output point requires the computation of only one polyphase filter output. With NαL master filter taps and L branches, the polyphase filter length is α, so that only α multiplies are required per output. Thus, the polyphase implementation saves a factor of LM multiplies over the standard implementation!