On two-part approximation in synthesis of pulse-shaping networks

A realizable transfer function providing the impulse response approximating a pulse of finite duration can be obtained using the following procedure. The function should be considered as consisting of the entire function (having no poles) of complex variable, and the delay multiplier. The entire function part representing spectral content of the impulse response is approximated by a finite degree polynomial. The delay multiplier is necessary for function realization by a lumped parameter circuit; the choice of delay multiplier defines the circuit realization. We propose the delay approximation which provides less error and results in the transfer function realizable by a passive LC-network. This approach is useful in realization of LC pulse-shaping circuit loaded by a resistor of transmitting antenna.