Evaluation Tests for Statistical Analyzers

摘要

This report describes a series of tests designed to evaluate the performance of statistical analyzers. The types of analyses that these analyzers typically perform and that must be evaluated are: (1) Instantaneous amplitude probability density, (2) Instantaneous amplitude probability distribution, (3) Negative instantaneous amplitude probability distribution, (4) Peak value probability density, (5) Expected number of maxima per unit time, (6) Expected number (total, positive, or negative) of threshold crossings per unit time, (7) Joint instantaneous amplitude probability distribution, (8) Joint instantaneous amplitude probability density, (9) Extreme value density, (10) Extreme value distribution. Tests with both periodic (sinusoidal and triangular) and random (broadband Gaussian, narrow band Gaussian, and clipped Gaussian) signal inputs are delineated for each of the above analysis modes. Tolerances on the output wave shapes of the periodic signal generators are described so that generators whose outputs will not contribute significantly to the measurement errors can be selected. It is suggested that the random test signals be recorded on magnetic tape so that the identical signals can be analyzed by the statistical analyzer and a digital computer. The digital computer analysis will accurately define the statistical properties of the actual test signal so that the problems associated with imperfections in the random noise generator and statistical uncertainty fluctuations can be avoided. The analytical derivation of all of the above statistical functions for sinusoidal input signals are included to illustrate the operating principles of this analyzer. (Author)