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.

[1]  Dario Petri,et al.  Effect of additive dither on the resolution of ideal quantizers , 1994 .

[2]  R. Gray,et al.  Dithered Quantizers , 1993, Proceedings. 1991 IEEE International Symposium on Information Theory.

[3]  John Vanderkooy,et al.  Quantization and Dither: A Theoretical Survey , 1992 .

[4]  A. G. Clavier,et al.  Distortion in a Pulse Count Modulation System , 1947, Transactions of the American Institute of Electrical Engineers.

[5]  Markku Renfors,et al.  Recursive implementation of FIR differentiators with optimum noise attenuation , 1996 .

[6]  Gabor C. Temes,et al.  Oversampling delta-sigma data converters : theory, design, and simulation , 1992 .

[7]  Kenzo Kamiyama,et al.  A Microprocessor-Controlled High-Accuracy Wide-Range Speed Regulator for Motor Drives , 1982, IEEE Transactions on Industrial Electronics.

[8]  Ludwik Liszka.  Measurements of line-of-sight velocities in prominences , 1970 .

[9]  Robert M. Gray,et al.  Quantization noise spectra , 1990, IEEE Trans. Inf. Theory.

[10]  Seppo J. Ovaska.  Improving the velocity sensing resolution of pulse encoders by FIR prediction , 1991 .

[11]  Robert M. Gray,et al.  Spectral analysis of quantization noise in a single-loop sigma-delta modulator with DC input , 1989, IEEE Trans. Commun..

[12]  L. Schuchman.  Dither Signals and Their Effect on Quantization Noise , 1964 .

[13]  M. Wagdy.  Effect of various dither forms on quantization errors of ideal A/D converters , 1989 .

[14]  A. Sripad,et al.  A necessary and sufficient condition for quantization errors to be uniform and white , 1977 .

[15]  William B. Fretter,et al.  Measurement of Velocity , 1963 .

[16]  R. Schreier,et al.  Delta-sigma data converters : theory, design, and simulation , 1997 .

[17]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[18]  R.D. Lorenz,et al.  High resolution velocity estimation for all digital, AC servo drives , 1988, Conference Record of the 1988 IEEE Industry Applications Society Annual Meeting.