Digital Analyzer for Statistical Moments: Design and Error Characteristics

A digital instrument is described that provides decimal readouts of the first four time-averaged moments and of the cumulative amplitude probability of a randomly varying voltage. There is no low-frequency limit, the upper-frequency being limited to about 6 kHz for a 99 percent confidence interval of 1 percent error. Measurements can be made in a one-cycle mode (for periodic inputs) or in a fixed-time or fixed-sample-size mode. Readouts of all the moments are available immediately at the end of the measurement time so that the instrument can be used for real-time applications. The voltage under measurement is sampled systematically and the samples are processed immediately using a weighted-feed logic system. The principles of operation and the design of the instrument are described. For many commonly encountered signals the overall error is within 1 percent for all four moments.