VLSI Digital Signal Processing Systems: Design and Implementation

10.10    PROBLEMS

1. Consider the direct-form 3rd-order IIR filter

   

   Pipeline this structure using clustered look-ahead pipelining for (a) 2- level, and (b) 4-level pipelining of each multiply-add operation. For each case, what are the poles of the new system? Are these pipelined systems stable?

2. Pipeline the IIR filter of Problem 1 using scattered look-ahead such that each multiply-add can be pipelined by 2 stages. Draw the complete structure, and pipeline this structure by placing latches at appropriate locations (you will need to break up multipliers into 2 segments). What are the poles of this system?
3. Consider the 2nd-order IIR filter with transfer function:

   

   Obtain a 3-stage pipelined transfer function using scattered look-ahead transformation. Specify the poles and zeros of this pipelined filter.

4. Consider the IIR digital filter transfer function

   

   Obtain an equivalent 4-level pipelined transfer function using (a) Clustered look-ahead and (b) Scattered look-ahead and decomposition approaches.

5. Consider the 2nd-order all-pole recursive filter

   

   This filter needs to be pipelined by 9 stages ...