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## 3.6    PROBLEMS

1. Consider the DFG shown in Fig. 3.20. Assume the time required for each operation is T.

Fig. 3.20    Data-flow graph for Problem 1.

(a)  What is the maximum achievable sample rate in this system?

(b)  Place pipelining registers at appropriate feed-forward cutsets such that the sample rate of this system can be approximately equal to 1/T. Clearly identify the feed-forward cutsets and count the total number of pipelining registers required.

2. Consider the IIR digital filter block diagram shown in Fig. 3.21. Assume that the multiplication operation takes 2 u.t. and the addition operation takes 1 u.t.

Fig. 3.21    Digital IIR filter for Problem 2.

(a)  Calculate the critical path of the IIR filter.

(b)  Pipeline the IIR filter by placing latches at appropriate feed-forward cutsets to reduce the critical path to 3 u.t.

3. Consider the nonrecursive signal processing structure shown in Fig. 3.22. Find an equivalent data-broadcast implementation of this algorithm to

Fig. 3.22    Data-flow graph for Problem 3.

improve the speed of the system. Do not use any additional latches. Calculate the throughput or sample speed of the broadcast architecture. (Hint: Transpose operation is ...

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