Of course there is one technicality: the elliptical approximations in
the previous two figures were perfectly consistent, but the double-elliptic
approximations were not. Muir's approximation did a much better job
in the dispersion-relation domain than it did in the impulse-response domain.
Figure 4 shows how the double-elliptic approximations
fit in the two different domains compare in the impulse-response domain.
Should we be concerned by this discrepancy?
Probably not, because this is a rather extreme example.
If there are no triplications the
approximations as fit in the two domains are much more nearly consistent,
as is demonstrated in Figure 5.