Phasing with 2nd-Order Allpass FiltersThe allpass structure proposed in  provides a convenient means for generating nonuniformly spaced notches that are independently controllable to a high degree. An advantage of the allpass approach even in the case of uniformly spaced notches (which we call flanging, as introduced in §5.3) is that no interpolating delay line is needed.
8.27. It is identical to that in Fig.8.23 with each first-order allpass being replaced by a second-order allpass. I.e., replace in Fig.8.23 by , for , to get Fig.8.27. The phaser will have a notch wherever the phase of the allpass chain is at (180 degrees). It can be shown that these frequencies occur very close to the resonant frequencies of the allpass chain . It is therefore convenient to use a single conjugate pole pair in each allpass section, i.e., use second-order allpass sections of the form
harmonic spacing of the notches, but what is the ideal non-uniform spacing? One possibility is to space the notches according to the critical bands of hearing, since essentially this gives a uniform notch density with respect to ``place'' along the basilar membrane in the ear. There is no need to follow closely the critical-band structure, so that simple exponential spacing may be considered sufficiently perceptually uniform (corresponding to uniform spacing on a log frequency scale). Due to the immediacy of the relation between notch characteristics and the filter coefficients, the notches can easily be placed under musically meaningful control.
Length Three FIR Loop Filter
Phasing with First-Order Allpass Filters