Page 251 - DSP Integrated Circuits

236 Chapters DSP Algorithms

The first step, according to the
procedure in Box 6.1, does not apply
since, in this case, there are no mul-
tiplications by -1. The second step is
to first assign node variables to the
input, output, and delay elements.
Next we identify and assign node
variables to the basic operations and
the nodes that correspond to the out- Figure 6.15 Second-order section in direct
puts (results) of the basic operations. form II
We assume that multiplication, two-
input addition, and quantization are
the basic operations. The resulting
variable assignments are shown in Figure 6.16.

Figure 6.16 Fully specified signal-flow graph with node variables

An operation can be executed when all input values are available. The input,
x(n), and the values stored in the delay elements, v\(ri) and v<z(ri), are available at
the beginning of the sample interval. Thus, these nodes are the initial nodes for
the computations. To find the order of the computations we begin (step 3) by first
removing all delay branches in the signal-flow graph. The resulting signal-flow
graph is shown in Figure 6.17.

Figure 6.17 Signal-flow graph with removed delay branches