Time-varying generalizations of all-pass filters

In many audio applications, digital all-pass filters are of central importance; a key property of such filters is energy (l₂ norm) preservation. In audio effect and sound synthesis algorithms, it is desirable to have filters that behave as all-passes with time-varying characteristics, but direct generalizations of time-invariant designs can lose the important norm-preserving property; for fast parameter variation, large gain increases are possible. We here call attention to some simple time-varying filter structures, based on wave digital filter designs, that do preserve signal energy and that reduce to simple first- and second-order all-pass filters in the time-invariant case.