Minimum-Phase/Allpass Decomposition

Every causal stable filter with no zeros on the unit circle can be factored into a minimum-phase filter in cascade with a causal stable allpass filter:

This result is easy to show by induction. Consider a single non-minimum-phase zero of . Then , and can be written with the non-minimum-phase zero factored out as

In summary, we may factor non-minimum-phase zeros out of the transfer function and replace them with their minimum-phase counterparts (not altering the amplitude response).

A procedure for computing the minimum phase for a given spectral magnitude is given in §12.4. More theory pertaining to minimum phase sequences may be found in [60].

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