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 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.