Cross correlation analysis improves time domain measurements

Abstract

The authors introduce several approaches to analyzing time-domain measurement data which the cross correlation to reveal data obscured by the measurement noise. They introduce cross-correlation-based variances (#/spl sigma//sup 2/) to estimate the Allan variance, the modified Allan variance, and the time variance in the presence of the measurement system noise. These variances substantially lower the short-term measurement noise floor; however, they require significantly more data. #/spl sigma//sup 2/ is also used as a tool to analyze and improve the measurement system noise. #/spl sigma//sup 2/ bears a precise relation to the three-cornered-hat /spl sigma/. The short-term noise floor for /spl sigma//sub y/(1 s) was reduced by a factor of 100 relative to the initial hardware and software configuration. The improvement described enable low noise measurements that were not possible earlier at 5 MHz.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>