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arXiv · 2003.07118

Cross-Spectrum Measurement Statistics

Antoine Baudiquez·Éric Lantz·Enrico Rubiola·François Vernotte
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Abstract

The cross-spectrum method consists in measuring a signal $c(t)$ simultaneously with two independent instruments. Each of these instruments contributes to the global noise by its intrinsec (white) noise, whereas the signal $c(t)$ that we want to characterize could be a (red) noise. We first define the real part of the cross-spectrum as a relevant estimator. Then, we characterize the probability density function (PDF) of this estimator knowing the noise level (direct problem) as a Variance-Gamma (V$\Gamma$) distribution. Next, we solve the "inverse problem" thanks to Bayes' theorem to obtain an upper limit of the noise level knowing the estimate. Checked by massive Monte Carlo simulations, V$\Gamma$ proves to be perfectly reliable to any number of degrees of freedom (dof). Finally we compare this method with an other method using the Karhunen-Lo\`{e}ve transfrom (KLT). We find an upper limit of the signal level slightly different as the one of V$\Gamma$ since KLT better takes into account the available informations.

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Antoine Baudiquez, Éric Lantz, Enrico Rubiola, François Vernotte. 2020-03-16. Cross-Spectrum Measurement Statistics. https://arxiv.org/abs/2003.07118

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