Quasi-Distortionless Filter Functions

If the first few central moments of a pulse-like function applied to the input of a filter are equated to the corresponding moments of the pulse-like output function, or if the input and output are expressed as power series in time and the first few coefficients of the two time series are equated (allowing for a constant multiplier and either a positive or negative delay), the general quasi-distortionless filter network function is specified. Such filter functions are derived and described in this paper. The simpler functions turn out to be easily realizable, practical, and minimum phase. They sometimes justify the maximally flat function as optimum in the quasi-distortionless sense and in other cases yield functions which are even better when compared on the basis of the gain-bandwidth product of an amplifier interstage system. Also, these functions make the mechanism of delay or prediction and operations (such as that of taking the derivative of an input signal) quite clear. The general approach of this of low frequency paper can be extended to arrive at end generalize the problem of low frequency compensation in low-pass amplifiers.