Fig. 5.3. Propagation delay across standard and saturation arithmetic constant coe cient multipliers implemented in Altera Flex10k70RC240-3

mentation, it is not necessary to use saturation arithmetic for all operators, so care must be taken to select the appropriate places and the appropriate degree of saturation to apply at those points. For systems with long impulse responses it may be possible, through judicious choice of saturator location and degree, to create a smaller implementation of the system using saturation arithmetic.

5.3 Preliminaries

The noise model for saturation arithmetic, presented in the following section, will involve the concepts of saturation nonlinearities, saturation systems and cross-correlations, which are defined below.

Definition 5.2. A saturation nonlinearity is a function of the form shown in (5.1). The parameter c > 0 is referred to as the cut-o of the saturation nonlinearity. (sgn(·) is the signum function, which has value -1 for negative argument, and +1 otherwise).