Another common method for increasing the density of an allpass impulse response is to nest two or more allpass filters, as described in §2.8.2 and shown in Fig.2.32 on page . In general, a nested allpass filter is created when one or more of its delay elements is replaced by another allpass filter. As we saw in §2.8.2, first-order nested allpass filters are equivalent to lattice filters. This equivalence implies that any order transfer function (any poles and zeros) may be obtained from a linear combination of the delay elements of nested first-order allpass filters, since this is a known property of the lattice filter .
In general, any delay-element or delay-line inside a stable allpass-filter can be replaced with any stable allpass-filter, and the result will be a stable allpass.