Page 243 - DSP Integrated Circuits

228 Chapter 6 DSP Algorithms

algorithm is a complex set of requirements that may be violated by even a simple
change in the algorithm. For example, intricate bit manipulations and nonlinear
operations are used in most speech coding systems. A simple change of the quanti-
zation scheme may drastically affect speech quality. In fact, the quality of most
DSP algorithms is strongly related to various finite word length effects. An even
more important aspect concerns the stability of the algorithm with respect to vari-
ous types of nonlinearities.
Recursive algorithms contain nonlinearities that may cause parasitic oscilla-
tions. Temporary malfunction of the hardware may also cause parasitic oscilla-
tions, as discussed in Chapter 5. Sophisticated theories and methods are therefore
invoked in algorithm design to assure that such oscillations cannot persist. Exam-
ples of filter algorithms that suppress all parasitic oscillations are wave digital fil-
ters and nonrecursive FIR filters. To avoid dangerous pitfalls, it is necessary to use
a design method that guarantees the integrity at each design step involved in
transforming the DSP algorithm into a working system.

6.2.2 Arithmetic Operations
At each level of system hierarchy it is convenient to define a set of basic operations
that can be executed on the PEs of that level. The operations are assumed to be
atomic and can not be further divided. Once an operation begins execution on a
PE, it will not be interrupted by another operation. Thus, these operations repre-
sent the smallest granularity of which parallelism can be exploited at the system
level.
The basic arithmetic operations used in the DSP algorithm can again be consid-
ered as lower-level algorithms acting on binary numbers, as illustrated in Figure 6.3.
Algorithms for realizing the arithmetic operations will be further discussed in
Chapter 11.
The properties of the arithmetic operations will determine the computational
properties of the algorithm at the next higher level in the system hierarchy. It is

Figure 6.3 Hierarchy of algorithms