System functions with minimum time-bandwidth product based on the higher order moments

Systems of finite order with minimum time-bandwidth products are considered. The time and frequency response spreads are defined by moments of the higher order in both domains. Minimizing the product of the moments, causal systems with the largest energy concentration in the time and frequency domain are obtained. The optimization is carried out for transfer functions up to the eighth order with two and four complex zeros. The moment orders are chosen from two to eight. The influence of the zeros and the moment order on system properties are considered. The complete data suitable for filter design are given.