Page 256 - DSP Integrated Circuits

6.5 DIFFERENCE EQUATIONS 241

Node Set Equations

Table 6.1 Difference equations in computational order for direct form II

explore this flexibility to minimize the amount of hardware resources required to
execute the algorithm.

In the method just discussed, a large number of simple expressions are com-
puted and assigned to intermediate variables. Hence, a large number of intermedi-
ate values are computed that must be stored in temporary memory cells and
require unnecessary store and load operations. If the algorithm is to be imple-
mented using, for example, a standard signal processor, it may be more efficient to
eliminate some of the intermediate results and explicitly compute only those node
values required. We demonstrate how this can be done by the means of an exam-
ple.

EXAMPLE 6.3

Show that some of the intermediate values can be eliminated in the system of dif-
ference equations derived in Example 6.2. Use the simplified system of difference
equations to write a Pascal program that implements the second-order section in
direct form II. The program shall emulate a data word length of 16 bits and use
saturation arithmetic.
Obviously, the only values that need to be computed explicitly are

Q Node values that have more than one outgoing branch
Q Inputs to some types of noncommutating operations, and
Q The output value.

The only node with two outgoing branches in Figure 6.25 is node UQ. The
remaining node values represent intermediate values used as inputs to one subse-
quent operation only. Hence, their computation can be delayed until they are