Design of wide-band amplifiers/filters using Lommel polynomials

The paper describes and analyzes a new class of filter/amplifier transfer functions. The denominator polynomials of these all-pole transfer functions are calculated via the sum of two Lommel polynomials R_n,μ(z) and R_n-1,ν(z) of orders n and n-1 with different indices μ and ν correspondingly. The proposed wide class of transfer functions may be considered as a generalization of Bessel transfer functions. Indeed for the particular choice of μ= 1/ 2 and ν= 3/ 2 the proposed filters are coinciding with Bessel amplifiers/filters. Using different values of μand ν allow one to modify the transfer function, obtain a desirable step-response overshoot and find the required overshoot- or rise-time-bandwidth exchange. This flexibility is especially useful for design of wideband amplifiers.