When a digital computer acts as an on-line computational device in a closed-loop measurement or control system, the performance is degenerated by the quantization errors incurred in reading continuous data into the machine. The analysis presented in the paper shows that the increase in steady-state mean square error introduced by this degenerative effect can significantly be reduced by employing non-uniform quantization of input data. The resulting deterioration in transient performance is negligible.
It is shown, under small signal conditions, that the spectrum of non-uniform quantization errors is essentially white. As a result, the expected maximum accuracy improvement in a given system can be easily evaluated. As a means of verifying the analysis, the performance of a practical direct digital control system employing non-uniform quantization is compared with a counterpart having uniform quantization. The steady state response to a spectral input shows an accuracy improvement equivalent to 7 bits.
The technique of non-uniform quantization described in the paper is readily implemented to improve the steady state accuracy of an existing system, or alternatively for a given design-consistent accuracy, to economize in analogue-to-digital converter bit capacity.