Page 366 - DSP Integrated Circuits

7.12 DCT Processor, Cont. 351

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PROBLEMS
7.1 Consider a 16-point ST-FFT.
(a) Determine which pairs of butterflies are computed in the two
alternatives discussed in section 7.3.2.
(b) Determine the range of the following indices: m, £]_, &uvs> &2> &2Ws> and p.
(c) Show how the computations of these indices can be simplified.
(d) What hannens if the index m is
incremented in Gray-order?

7.2 Modify the program in Box 7.2 so that four
butterflies can be computed concurrently.
7.3 Schedule the operations in the second-order
filter shown in Figure P7.3 so that T mi n is
reached. Figure P7.3. Second-order
(a) Assume T add = T mui t = I t.u. filter
(b) Assume T muit = 3 T add and T add = I t.u.
7.4 Assume that the adders have unit delay.
The times taken for the multiplications are
indicated in Figure P7.4. What is the
minimum sample period? Sketch a possible
scheduling of the PEs that yields a
minimum iteration period assuming that
the multipliers are nonpreemptive. How
many PEs are needed and what is their
degree of utilization?
7.5 (a) Derive the computation graph for the
maximally fast second-order section in
direct form II.
(b) Schedule the operations over one
sample interval so that the number of
concurrent operations is minimized. Figure P7.4