Rational transfer functions with minimum timebandwidth products.
H. Babić, Mladen Vučić · 2001
Transfer functions with finite zeros giving the minimum product of the impulse response duration and the frequency bandwidth are considered. The impulse response spread is characterized by the higher order moments. For the frequency spread measure, the second order moment is used. Minimizing products of the moments, causal systems with the largest energy concentration in time for a given bandwidth are obtained. The resulting impulse response is quasi Gaussian with small and short ringing. The transfer functions ' poles and zeros suitable for the filter design, up to the tenth order, are given.