Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

A collapse of the cross-spectral function in phase noise metrology



Craig W. Nelson, Archita Hati, David A. Howe


Cross-spectral analysis is a mathematical tool for extracting the power spectral density of a correlated signal from two time series in the presence of uncorrelated interfering signals. We demonstrate and explain a set of conditions where the detection of the desired signal using cross-spectral fails partially or entirely in the presence of a second uncorrelated signal. Not understanding when and how this effect occurs can lead to dramatic under-reporting of the desired signal. Theoretical, simulated and experimental demonstrations of this effect as well as mitigating methods are presented.
Review of Scientific Instruments


amplitude noise, cross-correlation, cross-spectrum, phase noise


Nelson, C. , Hati, A. and Howe, D. (2014), A collapse of the cross-spectral function in phase noise metrology, Review of Scientific Instruments (Accessed April 23, 2024)
Created February 25, 2014, Updated February 19, 2017