1.13 Computational savings of polyphase resampling

Computational savings of polyphase resampling

Recall the standard (non-polyphase) resampler in .

For simplicity, assume that $L> M$ . Since the length of an FIR filter is inversely proportional to the transition bandwidth (recalling Kaiser's formula), and the transitionbandwidth is directionally proportional to the cutoff frequency, we model the lowpass filter length as $N=\alpha L$ , where $\alpha$ 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 $N=\alpha L$ multiplies, giving a total of $\alpha LM$ multiplies per output.

In the polyphase implementation, calculation of one output point requires the computation of only one polyphase filter output. With $N=\alpha L$ master filter taps and $L$ branches, the polyphase filter length is $\alpha$ , so that only $\alpha$ multiplies are required per output. Thus, the polyphase implementation saves a factor of $LM$ multiplies over the standard implementation!