The effects of quantization noise and sensor nonideality on digital differentiator-based rate measurement

This paper focuses on the nature of the rate error which arises when a first-order digital differentiator is applied to the output of a uniform quantizer for the purpose of rate estimation. The quantizer input is assumed to be a constant-rate signal which is subject to a uniformly distributed noise source. New formulae are presented for the corresponding rms and spectral error characteristics. The results are applicable to the signal processing of sensor outputs, exemplified by the shaft encoder-based velocity estimation of an almost uniformly rotating mass. Both computer-generated finite data sets and experimental data derived from encoder-based shaft velocity measurements are utilized to verify the theoretical results. The results described are also applicable to a more general class of systems which involve the digital differentiation of quantized, noise-affected signals, such as first-order sigma-delta modulators with nominally constant input.