The phase response of a digital all-pass filter is often used to appro
ximate a prescribed phase or delay. Based on the nonlinear Tchebycheff
approximation theory, the phase and delay functions are investigated.
A number of necessary and sufficient (NS) conditions that characteriz
e the best approximation are obtained. Numerical design methods using
the phase or delay functions of a digital all-pass filter yield the mi
nimal unique global solution. A trigonometric rational function is der
ived for optimal approximation of a desired group delay. (C) 1997 Else
vier Science B.V.