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6.6 Computation Graphs 245
Figure 6.28 Computation graph for direct form II
graph correspond to execution time for operations and shimming and equalizing
delays in the computation graph.
6.6.4 Maximum Sample Rate
The maximum sample rate of an algorithm is determined only by its recursive
parts according to Theorem 6.2 [9, 23, 24]. Nonrecursive parts of the signal-flow
graph (e.g. input and output branches) generally do not limit the sample rate, but
to achieve this limit additional delay elements may have to be introduced into the
nonrecursive branches. This problem will be discussed in more detail in section 6.8.
Theorem 6.2
The minimum sample period for a recursive algorithm that is described by
a fully specified signal-flow graph is
where T opi is the total latency of the arithmetic operations etc. and NI is
the number of delay elements in the directed loop i.
The minimum sample period is also referred to as the iteration period bound.
Loops that yield T mi n are called critical loops. This bound can directly be found
from the signal-flow graph by inspection. The maximum sample rate can also be
found from the intrinsic coefficient word length [28].
