Recursive and Non Recursive Realisation:

In recursive realisations, the present output value depends on the input (past and present values), as well as the previous value of the output. It can usually be recognized by the presence of both a and b terms in the input and output rela­tionship [Eq. (15.79)].

The recursive realisation is illustrated in Fig. 15.31(a). Since the impulse response of recursive filters extends to infinity, this realisation is particularly suited for implementation of IIR filters. In non-recursive realisation, the present value of the output depends only on the present and past values of the input.

Equivalently, the coefficients b in Eq. (15.79) are zero for this case. A typi­cal realisation is shown in Fig. 15.31(b). Since the impulse response yielded by this type of realisation if finite, the resulting filters are always stable, in contrast to the possible instability of filters resulting from recursive realisation.