Improved quantization error characteristics in FIR differentiators using irregular sampling

It is shown that irregular sampling can be used to advantage in FIR differentiators for quantized systems, by reducing the maximum error caused by input quantization. Formulae are derived for 1) the filter coefficients that correspond to minimum average mean-squared output error, given white noise at the input; and 2) the mean-squared error of the quantized system in the important constant-rate case. Comparisons between system performance for regular and irregular sampling are presented for one simple sampling strategy. The differentiators have been used to advantage as velocity estimators in motion control systems, but have wider application.