The efficient implementation of IIR decimation and interpolation filters can be achieved with polyphase structures. Developing a polyphase structure requires the decomposition of the filter transfer function into a set of M ( L) polyphase components as already demonstrated in Chapter IV for FIR filters. The overall filter transfer function of a decimation filter H( z) is represented in the form

where H _k( z) is the kth polyphase IIR subfilter. For an interpolator, the representation of (5.11) is also used including the multiplication by L,

In the case of FIR filters the transfer function is a polynomial in terms of z ^?1, and consequently the polyphase decomposition is very simple as shown in Chapter IV. However, the transfer function of an IIR filter is the ratio of two polynomials, and therefore, the representation of such a function in the form of equations (5.11) and (5.12) requires modifications of the original transfer function in such a way that the denominator contains only powers of z ^M ( z ^L).

There exist in the literature several methods for the polyphase decomposition of the IIR filter transfer function. The well known technique based on the rearrangement of the original IIR transfer function to obtain the form of (5.11) and (5.12) was proposed by Belanger, Bonnerot, and Coudreuse (1976). This technique develops the polyphase Subfilters H _k( z ^M) starting from the given transfer...