Algorithms and Parallel Computing

14.15 POLYPHASE INTERPOLATOR IMPLEMENTATIONS

A polyphase decimator splits the high-rate input signals into M low-rate nonstreams such that each stream is applied to a filter with length N/M. Figure 14.17 shows the splitting of the input data stream into M nonoverlapped streams. Each filter has the following characteristics:

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

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

3. Every Lth input sample is used.

Figure 14.17 Dependence graph for polyphase filter h₀(nT′) for a 1-to-L interpolator for the case when L = 3 and N = 12.

In order to get a dependence graph for a polyphase filter, we break up the dependence graph of Fig. 14.1 into M = 3 DAGs as shown in Fig. 14.18. Each dependence graph corresponds to one branch of the polyphase filter structure of Fig. 14.17. Table 14.2 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 < L) produces the ith upsampled stream and uses the filter coefficients h_i+jM where 0 ≤ j < N/L. The advantages of polyphase filters is that each filter operates at the slower rate of LT and its length is N/L. We can use the different 1-D FIR filter structures discussed previously to realize the polyphase decimator.

Table 14.2 Filter Coefficients ...