Abstract
The increasing requirements for probability density measurements of the amplitude characteristics of time-varying signals require a careful examination of (1) requirements for probability density analyzers, (2) techniques of measurement, and (3) uncertainty in estimates obtained from samples of finite duration. Requirements discussed include bandwidth and dynamic range, amplitude sampling interval (window width), and necessary readouts. Various techniques of using a probability density analyzer are discussed, with emphasis on the necessity of using different techniques for different types of data and/or use thereof. A method of scanning that guarantees constant uncertainty over the entire range of the probability density is described. An expression for the uncertainty of the measured probability density as a function of sampling time is obtained, and measurements are shown indicating the relationship of sampling time, window width, bandwidth, and probability density to the uncertainty. The normalized variance is shown to be of the form σ2=K/[foTΔxw(x)]. The constant K is derived, using alternate assumptions, and is evaluated experimentally. The analysis in this paper is supported by measurements made with, and on, a commercial probability density analyzer.
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