Coupling between Sample Rate and Required Wordlength for Finite Precision Controller Implementation with Delta Transform

The delta-transform has been shown to have superior numerical properties in high sample rate controller implementation and signal processing. However, similar to controller design and implementation in the shift-operator, finite precision implementation introduced coupling between the required wordlength and the sample rate. As the sample rate changes, the locations of poles and zeros fluctuate from grids to grids. Insufficient precision of the processor may results in undesirable characteristics or even unstable controller. In this paper, we analyze this coupling and propose conservative upper bounds on the sample rate given a controller representation, lowest frequency of interest and the available wordlength. In addition, we will also develop specific guidelines to estimate the required precision given a controller representation, frequency of interest and sample rate. Numerical examples are presented to verify the applicability of the proposed bounds.