Algorithms and Parallel Computing

14.8 POLYPHASE DECIMATOR IMPLEMENTATIONS

A polyphase decimator splits the high-rate input signals into M low-rate nonoverlapped streams such that each stream is applied to a filter with length N/M. Figure 14.8 shows the splitting of the input data stream into M nonoverlapped streams, and each stream is fed to a low-pass FIR filter. Each filter has the following characteristics:

1. It operates at the longer sample time T′ = MT.

2. The number of filter coefficients is reduced to N/M.

3. Every Mth input sample is used.

Figure 14.8 Polyphase implementation of a decimator for the case M = 3.

In order to get a dependence graph for a polyphase filter, we break up the dependence graph of Fig. 14.1 into M = 3 dependence graphs. Figure 14.9 shows the dependence graph corresponding to the stream feeding the filter h₀(nT′). Each dependence graph corresponds to one branch of the polyphase filter structure of Fig. 14.8. Table 14.1 shows the filter coefficients associated with the filter whose impulse transfer function is h_i(nT) and also shows the stream of input data samples allocated to it. In general, polyphase filter h_i(nT) (0 ≤ i < M) is fed the ith downsampled stream and uses the filter coefficient h_k+jM where 0 ≤ j < N/M and is given by

(14.26)

Table 14.1 Filter Coefficients and ...