Digital all-pass networks

A systematic method is outlined to realize an
m
th-order all-pass digital transfer function using only
m
multipliers as a cascade of first-order and/or second-order all-pass sections. The realization is based on the multiplier extraction approach in which the
n
th-order filter section is considered as a digital
(n + 1)
-pair of which
n
pairs of input and output terminal variables are constrained by
n
multipliers. The transfer matrix parameters of the digital
(n + 1)
-pair, containing only delays and adders, are first identified from which the realization is obtained by inspection. Both canonic and noncanonic realizations are derived. All realizations are then compared with regard to the effect of multiplication roundoff and hardware requirements.