Development of Visual and Numerical Methods Based on Second Order Statistics for the Analysis of Digital Measurement Records

Abstract

In this paper some methods developed by the author for the analysis of measurement time series containing the equally spaced sampled values of continuous-time phenomena having stable probabilistic character are introduced. The neighbourhood figure gives information about the smoothness of the record with the visualization of the second order probability density function of its nearest neighbouring values. It can be used for the fast preliminary checking of the time series. For the quantification of the visual information the neighbourhood number, a dimensionless frequency scale parameter characterizing the short-term changing rate of the record, is defined. It is suitable for the numerical rating of the smoothness of the time series and for the evaluation of the applied sampling frequency in comparison with the character of the sampled continuous function. The neighbourhood function can be used for the detection of the presence of random measurement errors. Although it gives complementary information with the autocovariance function, it is sensitive for the small deviation instead of the correlation. A method based on the extrapolation of the autocovariance function is also introduced for the numerical estimation of the magnitude of the measurement inaccuracies.