Direct synthesis of filter transfer functions

In this paper we propose a new procedure for the direct synthesis of complex transfer functions for a new class of selective filter. Conditional mean square approximation with Cheby¿shev weights, with three Lagrangian multipliers (for transfer-function values at cutoff frequency, at the origin (¿ = 0) and for the phase at the cutoff frequency) gives a new class of filter derived in explicit form. By the choice of the transfer-function phase we can control the shape of amplitude characteristic in the passband or the filter selectivity.