Polyphase Structure for IIR Filters The anti-aliasing filter in a decimator and the anti-imaging filter in an interpolator may each be either an FIR or an IIR filter. The polyphase structure can be developed for any filter, FIR or IIR, and any finite value of M. We now proceed to the case where h(n) is an infinitely long sequence:

Once again we arrange the terms into M groups or branches in a modulo-M fashion. Each branch contains infinitely many terms. The terms are arranged in tabular form below:

Define

This is called the M-component polyphase decomposition of H(z). The M functions Pm( z) are the polyphase components of H(z). This overall operation is known as polyphase filtering.  As an example, for M = 3, we have 

We may also rearrange the output equation as

This last equation leads to the polyphase structure shown above, known as the transpose polyphase structure because it is similar to the transpose FIR filter realization.

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