Structure-induced low-sensitivity design of sampled data and digital ladder filters using delta discrete-time operator

The concept of the delta discrete-time operator-based doubly terminated two-pair (ladder) is discussed here for use in sampled-data and digital filter design. The two-pair filter utilizes traditional backward Euler and forward Euler integrators, is lossless under scaling (LUS), and possesses good magnitude sensitivity which is induced intrinsically due to the filter structure. This paper is an overview and consolidation of results published by the authors over the years in various conferences (Khoo et al., 1998, 1999, 2001, 2008, 2008a, 2008b) in a unifying and tutorial fashion. To achieve the low magnitude sensitivity, the well-known Feldtkeller equation corresponding to the delta-operator formulation is derived to establish the theoretical basis for the realization. One significant advantage of the design procedure presented here using the delta operator is that it overcomes the numerical problem at the spectral factorization stage of the conventional z-domain lossless-discrete-time integrator (LDI) synthesis method when the filter poles are clustered around z = 1. Furthermore, the entire operation involves only rational polynomials, as opposed to fractional power polynomials as in the LDI and other methods in z-domain. The method presented can realize three distinct forms of transfer functions with varied transmission zeros.