Optimum weights in delay equalization

In network design practice it is quite typical to design a network having a suitable amplitude response and to follow this with a network having unit amplitude response whose purpose is to modify the phase response so that the total network meets requirements on the phase response. Such phase-correcting networks are called all-pass delay equalizers. Their design amounts to function approximation of a special form. It is common practice to design equalizers so that the residual error in the envelope delay
(d\phi/d\omega)
has an equal ripple characteristic (constant weight function). The resulting residual distortion has a form which can be interpreted in a television system as two "ghosts" displaced in time from the desired signal by an amount inversely proportional to the ripple frequency. We determine a weight function, dependent upon the spectrum of the signal being processed, which minmmizes the power in these "ghost" distortions. These results are illustrated by application to example networks and signals.