We have seen in Chapter IV that in the case of an FIR decimator and interpolator, the computational requirements are reduced by the factor of M, and by the factor of L, respectively. The same order of computational savings cannot be achieved with IIR decimation and interpolation filters. This is due to the fact that computations at the lower sampling rate can be evaluated only in the nonrecursive part of the system as demonstrated in the preceding section and illustrated in Figures 5.2 and 5.4.

Considering the structure of decimator in Figure 5.2, we derive easily the corresponding multiplication rate, which we denote by R _M,IIR-DEC. The multiplication rate R _M,IIR-DEC is expressed in multiplications per second. We conclude that the computation rate for a factor-of- M decimator consisting of an N ^th order IIR filter followed by a factor-of- M down-sampler is determined by the expression,

On the other hand, considering the interpolator structure in Figure 5.4, we derive the multiplication rate for the L-fold interpolator denoted with R _{M-IIR_INT},

The following example illustrates the computational complexity of an IIR factor-of-5 decimator implemented in the direct form according to Figure 5.2. We compute the multiplication rate of the IIR decimator and compare the result with the multiplication rate of the corresponding factor-of-5 FIR decimator.