Some Relations Between Frequency and Time Domain Errors in Network Synthesis Problems

Bounds are derived for frequency and time-domain errors of a transient synthesis problem. The maximum error produced by a general input is related to the error of the impulse input. By considering distributions, a meaning is proposed for the time-domain error in the case when the error-transfer function is not Fourier-transformable in the ordinary sense. Rectangles and bell-shaped curves are used in approximating the error-transfer function.