Maximally-flat rational approximation with multiple critical pole-pair

The class of lowpass rational transfer functions, with a multiple critical pole-pair, equiripple in the stopband and maximally flat at the origin, is investigated and tables of poles and zeros of an adequate number of functions are supplied. With respect to the classical inverse-Chebyshev functions, the proposed functions allow the solution of the approximation problem, with a remarkable reduction of the highest pole Q-factor, at the expense of a typical order-increase equal to 1. In more favourable situations, it may happen to satisfy the specification with no increase in the order