Chebyshev approximation of a constant group delay with constraints at the origin

This paper deals with low-pass filter functions approximating a constant delay in an equiripple manner which does not yield a standard delay error curve. This type of Chebyshev approximation is obtained by imposing a constraint on the error curve at . It is shown that using the constrained approximation, the delay approximation bandwidth for odd and a prescribed ripple factor may be equal to, or even larger than, that obtained by Abele\´s polynomials; the latter solution is neither unique nor the best approximation. The magnitude characteristics of the constrained approximants are very much improved and the transient responses to a unit step input compare favorably with those for the other known systems including Schüssler\´s functions with equiripple step response. Tables are presented which include the pole locations of some selected constrained approximants of 3, 5, 7, and 9 degrees, the comparative stopband attenuation relative to the Abele case, and the most important quantities associated with a step response.