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9.5 Implementations Based on Complex PEs 397

9.5 IMPLEMENTATIONS BASED ON COMPLEX PEs

Arithmetic operations in most DSP
algorithms generally involve several
inputs and operations with only one or
a few outputs [31, 34-38]. Typical
examples are butterflies, two-port
adaptors, and sum-of-products. Hence,
basic PEs should be of the type illus-
trated in Figure 9.11. Figure 9.11 Typical DSP processing element
The basic approach is to
use a dedicated PE for each
value in the algorithm that
has to be computed explic-
itly. We will discuss the
selection of these values
later. It is often advanta-
geous from a chip area point
of view to use high-speed
bit-serial communication
between the PEs and broad-
cast the outputs from the
multiple-input PEs via a bit-
serial network, as shown in
Figure 9.12. A bit-serial net-
work requires less area and
Figure 9.12 Fully parallel architecture with a
power.
minimum number of PEs
fc»ucn an architecture
has a minimum number of
PEs and a large granularity. It can easily be time-shared between many input sig-
nals by expanding the memory. However, in many applications the required num-
ber of PEs from a computational point of view is less than the number of
expressions. The processing elements are therefore not fully utilized. In such cases
a more elaborate scheme having a few multiplexed PEs may be considered. This
approach is efficient when the DSP task fully exploits the processing power of the
PEs. In fact, when the PEs are time-shared among many input signals, this is one
of the most efficient approaches available for implementation of high-performance
digital filters.

9.5.1 Vector-Multiplier-Based Implementations

The basic operation used in digital filters and many other DSP algorithms is the
sum-of-products

which also can be viewed as a vector multiplication, or inner product, or dot prod-
uct, between a constant vector a and a data vector x. The latter type of vector