Investigation of systematic noise in stochastic linear system analysis

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Abstract
In stochastic system analysis, transfer functions are retrieved from experimental data by cross correlation. A well‐known linear cross correlator is the Michelson interferometer used in Fourier transform infrared spectroscopy. Due to the noise excitation, the transfer functions are inherently contaminated by systematic noise. It is shown, that in the limit of observation periods which are long compared to the maximum time shift in the cross correlation, the systematic noise decreases in proportion to the inverse square root of the data‐acquisition time. Experimental data from stochastic NMR spectroscopy illustrate that the resolution of the transfer function can be optimized independent of the observation period.