Filter design for optimal transient performance

A filter design method which takes into account the filter's behavior during its transient period, rather than being based on steadystate frequency response, is proposed. The performance of the filter is expressed as a function of its response to sinusoids of varying frequency but fixed duration, thus leading to a treatment of the problem by the methods of optimal control theory. It is shown that if the magnitude of the filter impulse response is required to be bounded, then the magnitude of the optimal impulse response assumes the bound at all times, independent of the particular performance criterion used.