Finite-precision characterization of a class of Bode-type variable-amplitude digital bump equalizers

In a previous contribution, a set of realizability conditions was developed and applied to the design and enumeration of variable-amplitude digital bump equalizers. This paper is concerned with an investigation of the performance characteristics of these digital equalizers taking into account the non-ideal effects of finite-precision arithmetic. The necessary and sufficient conditions for the BIBO stability of these equalizers under infinite-precision arithmetic has been established in a recent paper. This paper, on the other hand, applies the results thus obtained to the development of a class of equalizers based on finite-precision characteristics and a technique for the selection of equalizers from this class based on the determination of the required internal signal wordlength to ensure guaranteed stable operation without overflow saturation and limit-cycles under finite-precision arithmetic