Multiple-pole-and-zero approximation of general attenuation specifications

A new approximation method is proposed to realize transfer functions in which the multiplicity of each real pole (zero)- and complex pole (zero)-pair may be imposed by the designer. These functions may be evaluated to satisfy any assigned attenuation specification, and, hence, allow the design of filters by cascading low-order blocks with lower -factors, compared with the usual simple-pole solutions. This result is very practicable in the construction of highly selective -active filters. A complete algorithm is implemented to evaluate these functions.