Page 290 - DSP Integrated Circuits

Problems 275

The pipeline shall have three stages. By how much is the maximum sample
frequency increased?
6.25 Determine the transfer function and the corresponding difference equation
for a pipelined second-order all-pole section using
(a) Clustered look-ahead pipelining,
(b) Scattered look-ahead pipelining.
The pipeline shall have three stages. By how much is the maximum sample
frequency increased?

6.26 Derive the structures in Problem 6.25 in transposed form. Compare the
advantages of the original and the transposed structures.
6.27 Discuss the relationships between the following concepts: pipelining, latency,
sampling period, throughput, number of resources, and their utilization.
6.28 There are three distinct and possibly complementary ways to increase the
maximum throughput of a recursive algorithm. Discuss the various versions
of these ways.
6.29 The signal-flow graph shown in Figure P6.29 is a i *T*\— a
part of a larger graph.
(a) Determine the maximum sample frequency
when a multiplication takes two time units r^n (+>-*
and an addition takes one time unit. T ^r
(b) Modify the graph so that the true maximum
sample frequency is attained. ,—I—I (* H C
T ^~~r
6.30 Determine the maximum (output) sample
frequency that can be achieved by the
&*-*
interpolator discussed in section 6.10.
6.31 (a) Derive the system of difference equations for Figure P6.29.
the filter in Figure 6.30 when it is being used
for decimation with a factor of two.
(b) Derive the corresponding state-space representation.
(c) Derive a scheme based on block processing to process two samples at a
time.