Systems with minimum time-bandwidth product based on the higher order moments
H. Babić, Mladen Vučić · 2000
Time functions whose duration and bandwidth are as small as possible have practical as well as theoretical interest. Many criteria are employed for calculation of such time functions. Moments of the impulse response and moments of the frequency response can be used for characterization of response time and frequency band. The second moments were used for the definition of the uncertainty principle. In this paper response functions of finite order systems are characterized not only by the second but also with fourth, sixth and eight moments. To find out properties of obtained functions and values of time frequency band products, a numerical optimization is carried out for all-pole transfer functions, up to the eight orders. Properties of obtained systems are given and compared.