Filters with variable order and virtually independent time delay

An all-pole filter and a filter with a rational transfer function are considered, both of which are generalizations of the Bessel filter. It is shown that by properly selecting the generalizing parameters, the time delay in each case is, for low frequencies, very nearly independent of the order of the filter. It is possible, also, to select the parameters so that a nearly constant time delay is maintained for low frequencies while the filter order is varied to obtain a number of amplitude responses.