A modification of the Bessel filter

The continued fraction used to obtain the transfer function of the Bessel filter is modified by adding a parameter
a
>
-1
to the odd integers in the expansion. The resulting transfer function is realizable and has a time delay at
\omega = 0
which is independent of the order of the filter, and which may be varied from 0 to
\infty
by changing
a
. A further modification yields transfer functions from continued fraction expansions involving the even integers and the positive integers.