Microwave filters with flat time delay both in passband and stopband

An exact method is presented to find a new class of parametrical polynomials which provides
(n - m)
zero derivatives of relative delay at
p = 0
and
m
zero derivatives about
p = \infty
. Explicit expressions of the polynomials for
n = 2,3,4,5
, and
6
(and for
0 \leq m \leq n
) are derived from a linear second-order differential equation. Among the possible applications of these polynomials we show their interest in equalizing a class of microwave filters and for design of multiplexing systems.