Recovering the spectrum of a low level signal from two noisy measurements using the cross power spectral density

The article describes a method for estimating the spectrum or RMS value of a low-level signal corrupted by noise. If two identical sensors can be employed simultaneously and the additive noise sources are uncorrelated, the cross power spectrum can recover the power spectrum of the underlying signal. When using the Welch method to estimate the cross power spectrum, the estimation process is shown to be biased but consistent, with a variance that is inversely proportional to the number of data sets. The proposed technique is demonstrated experimentally to recover the vibration spectrum of a piezoelectric cantilever. The dual sensor method reduces the effective noise floor by three orders of magnitude and recovers spectral features that were otherwise lost in noise.