Pulse-forming networks using generalized Laguerre polynomials

A new class of all-pole transfer functions for pulse-forming networks based on the use of generalized Laguerre polynomials is introduced. It is shown that the two variable parameters, which are available with the generalized Laguerre polynomials, can always be adjusted so as to obtain an impulse response with any prescribed attenuation of transient overshoots. These filters, which may be referred to as generalized Laguerre filters, are shown to include as special cases Bessel filters, Gaussian filters and a recently derived class of transitional filters utilizing modified Bessel polynomials. A comparison with the Schiissler filters, designed for impulse response with equal ripple transient ringing is also presented. Tables are presented giving the pole locations of these filters for n = 3¿7 and the transient overshoot attenuation of 20¿60 dB in steps of 10 dB. Normalized element values for LC ladder realization with equal resistance terminations are also included.