Implementation and error analysis in digital filters based on digital incremental computers

Sensitivity and roundoff errors can seriously limit the application of recursive digital filters in practice, particulary when the filter have poles near z = +1. A filter structure, based on digital incremental computers, is proposed which has low sensitivity, good error characteristics, and simple hardware implementation for pole locations close to z = +1. A design procedure was suggested to implement the filter structure given the transfer function to be realized, and the relations among roundoff errors, dynamic range, and the size of the hardware multiplier are discussed. Implementing high order digital filters was also considered and simulation results are presented. In short, the structure was found to be matched to transfer functions which have all their poles clustered around z = +1.