For studying the efficiency of IIR decimators and interpolators let us consider the factor-of- M decimator depicted in Figure 5.1, where the decimation filter H(z) is an N ^th order IIR transfer function.

Figure 5.1: General structure of factor-of-M decimator

For an IIR decimation filter, the H( z) is the transfer function of the form

where A( z) and B( z) are N ^th order polynomials in z ^?1,

The input-output relations (5.1) can be rearranged in a product of the recursive section 1/ A( z) and non-recursive section B( z),

Denoting the output of the recursive part with W( z), i.e.,

we present relation (5.3) as the output of the nonrecursive part inputted by W( z),

In time domain, input-output relations (5.4) and (5.5) are expressed by the difference equations,

The recursive equation (5.6) computes the intermediate sequence { w[ n]}, which is used in the nonrecursive equation (5.7) for computing the output samples v[ n].

For computing the decimated sequence { y[ m]}, we compute only every M ^th sample of { v[ n]}, i.e.,

Equation (5.8) shows that for computing a single sample in { y[ m]} we use N+1 consecutive samples of { w[ n]}. Therefore, the computations can be evaluated at the...