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6.2 DSP Systems 227

Figure 6.2 The three parts of an algorithm

Generally, a DSP algorithm can be described by a set of expressions, as shown
shortly. The sign ":=" is used to indicate that the expressions are given in
computational order.

Note that the arguments on the right-hand side of the two first expressions
contain only old (i.e., known) values. These two expressions can therefore be com-
puted immediately. Once these have been evaluated, the remaining expressions
can be computed successively.
DSP algorithms can be divided into iterative processing and block processing
algorithms. An iterative algorithm performs computations on a semi-infinite
stream of input data, i.e., input data arrive sequentially and the algorithm is exe-
cuted once for every input sample and produces a corresponding output sample.
The period between two consecutive iterations is called the iteration period or sam-
ple interval. In block processing, a block of output samples is computed for each
input block, which results in a large delay between input and output. Block process-
ing is commonly used for DSP algorithms based on matrix operations, but it can
also be used to increase the maximum sample rate. Block processing algorithms
can be used if the input samples arrive in batches (blocks) or in non-realtime appli-
cations. Here we will mainly discuss the former type of algorithm which is charac-
terized by the following properties:
Q The input and output data rates are high.
Q The input and output values are synchronized with the sample period.
Q The sequence of operations is data independent.
Q The algorithm must be executed periodically.
Q Hard real-time operation with a deadline equal to the sampling period.
On the surface, most DSP algorithms look very simple since they consist of a
set of basic arithmetic expressions evaluated repeatedly. Complicated data struc-
tures are seldom used. These facts are often misunderstood by novice hardware
designers who may be tempted to modify an algorithm to suit the idiosyncrasies of
the hardware, design techniques, or tools. Such uninitiated and sometimes undoc-
umented changes of the algorithm must be avoided, since underlying the DSP