Ripple-pass function

The well-known relation for an all-pass function is generalized by the introduction of two parameters
k_{a}
and
k_{b}
making
F(s)=\frac{EvP(s)-k_{a}OdP(s)}{EvP(s)+k_{b}OdP(s)}
where
P(s)
is a Hurwitz polynomial, while
EvP(s)
and
OdP(s)
are its even and odd parts, respectively. It is shown that the amplitude, phase, and group delay of such a generalized all-pass function ripple, and that the ripples are dependent on the two introduced parameters and their ratio
K = k_{a}/k_{b}
. Thus the name "ripple-pass function." Some interesting and important features of the discussed function have been considered here. The ripple-pass function is suitable for practical applications such as amplitude, phase, and/or delay equalization, or for design of narrow-bandpass or bandstop (notch) filters. The ripple-pass function can be easily realized by using simple passive and active networks.