The following figure shows the polyphase decimation filter option which implements the computationally efficient M-to-1 polyphase decimating filter.
A set of N prototype filter coefficients is mapped to the M polyphase subfilters according to the following equation.
The polyphase segments are accessed by delivering the input samples x(n) to their inputs using an input commutator which starts at the segment index i = M-1 and decrements to index 0. After the commutator has executed one cycle and delivered M input samples to the filter, a single output is taken as the summation of the outputs from the polyphase segments. The output sample f ′s rate is f ′s = fs/M where fs is the sample rate of the input data stream (n), n = 0, 1, 2,…. .
Observe that each of the polyphase segments is operating at the low output sample rate f ′s (compared to the high input sample rate fs), and a total of operations is performed per output point.