Prior knowledge of the autocorrelation function (ACF) enables an application of analytical formalism for the unbiased estimators of variance s2a and variance of the mean s2a(xmacr;). Both can be expressed with the use of so-called effective number of observations neff. We show how to adopt this formalism if only an estimate {rk} of the ACF derived from a sample is available. A novel method is introduced based on truncation of the {rk} function at the point of its first transit through zero (FTZ). It can be applied to non-negative ACFs with a correlation range smaller than the sample size. Contrary to the other methods described in literature, the FTZ method assures the finite range 1 < neff ≤ n for any data. The effect of replacement of the standard estimator of the ACF by three alternative estimators is also investigated. Monte Carlo simulations, concerning the bias and dispersion of resulting estimators sa and sa(×), suggest that the presented formalism can be effectively used to determine a measurement uncertainty. The described method is illustrated with the exemplary analysis of autocorrelated variations of the intensity of an X-ray beam diffracted from a powder sample, known as the particle statistics effect.

Direct sensor-to-microcontroller is a simple approach for direct interface of passive modulating sensors to a microcontroller without any active components in between the sensor and the microcontroller and without an analog to digital converter. The metrological performances of such interface circuits are limited by certain microcontroller parameters which are predetermined by the manufacturing technology. These limitations can be improved by specific hardware-related techniques and can improve the accuracy, speed and resolution of the measurements. Such hardware solutions as well as proper selection of the electrical components are addressed in this paper. It has been shown that employment of only a few MOSFET transistors can reduce the maximal relative error of single point calibration more than fifteen times and can increase the measuring speed around 30 % in all calibration techniques in the measurement range of PT1000 resistive temperature sensors. Moreover, the effective number of resolution bits increases by more than 1.3 bits when using an external comparator.