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Computational Savings of Polyphase Resampling

Module by: Phil Schniter. E-mail the author

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Computational Savings of Polyphase Resampling

Recall the standard (non-polyphase) resampler in Figure 1.

Figure 1
Figure 1 (m10443fig4.png)

For simplicity, assume that L>MLM . 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=αLN αL, where αα is a constant that determines the filter's (and thus the resampler's) performance (independent of LL and MM). To compute one output point, we require MM filter outputs, each requiring N=αL NαL multiplies, giving a total of αLM αLM multiplies per output.

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

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