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Variance of random signal mean square value digital estimator

Lal-Jadziak J., Sienkowski S.

Metrology and Measurement Systems

2009

Vol. 16, nr 2

267-277

In the article, original relations enabling the estimation of the variance of a random signal mean square value digital estimator are derived. Three cases are considered: first when the estimator is determined from quantized samples; second, when it is additionally assumed that the conditions of Widrow's theorem are satisfied; and third, when the samples have not been quantized. The obtained relations can be used e.g. to determine uncertainty in precision measurements and to evaluate signal degradation in radio astronomy. As an example, the variance of the mean square value estimator of a random Gaussian signal for the three above-mentioned situations is analyzed. It has been observed that in the first and second cases, an increase in variance as well as in type A standard uncertainty takes place in comparison with the estimation based on unquantized samples. This increase diminishes along with an increase in the ratio of the signal rms value to the quantization step size.