but are they consistent?

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  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 .