On the Transfer Function Error of State-Space Filters in Fixed-Point Context

This brief presents a new measure used for the implementation of filters/controllers in state-space form. It investigates the transfer function deviation generated by the coefficient quantization. The classical L ₂-sensitivity measure is extended with precise consideration on their fixed-point representation in order to make a more valid measure. By solving the related optimal realization problem, fixed-point accurate realizations in state-space form can be found.