Why is *Delay(theta-dt/2, ...) better?

[arvoelke]

Both PadeDelay(theta-dt/2, ...) and LegendreDelay(theta-dt/2, ...) better-approximate the delay line of theta. But this is only significant/visible at large values of dt and q. This may have something to do fundamentally with the use of [q-1/q]-order approximants, which removes the passthrough.

[arvoelke]

May also be connected to the use of ZOH: dt/2 is the mid-point within the interval over which the step is held constant.