Optimum flat delay filter characteristics
Khee Khok Pang, Paul A. Kirton · International Journal of Circuit Theory and Applications · 1982
Abstract The problem of finding optimum filter characteristics that produce flat delay in the passband is formulated as a convex programming problem for minimum‐phase lowpass filters. The flatness of the group delay is indicated by an error norm, which is a measure of the deviation of delay characteristic from a constant reference level. When the attenuation specifications are relaxed, it is possible to achieve a constant delay characteristic and the problem is solved analytically. When the attenuation constraints are too tight to achieve the constant delay characteristic, the problem is solved numerically. If the least squares error criterion is used, the problem is a quadratic programming problem. It reduces to a linear programming problem for the minimax criterion. Some resulting optimum attenuation characteristics and their associated error norms are given. The tabulated error norms represent the lowest theoretical limits that lowpass, minimum‐phase filters can ever attain. This is confirmed by comparing the limits against the performance of some well‐known filters.