Sensitivity Enhancement in Magnetic Resonance. I. Analysis of the Method of Time Averaging

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Abstract
A theoretical analysis of the method of time averaging is made with special emphasis on the correlation effects caused by non‐white noise. It is shown that only in special cases is the signal‐to‐noise ratio improved exactly according to the square root of the number of successive scans through the investigated spectrum. This is shown in detail for random noise with an exponential‐cosine autocorrelation function. In the case of random noise with a pure exponential autocorrelation function, the deviation from the proportionality to the square root of the number of scans does not exceed a factor √2. If the frequency dependence of the power spectrum of the noise is given by |f|−λ, 0≤λ≤1, then the proportionality to the square root of the number of scans holds exactly. A peak in the noise power spectrum at a multiple of the repetition frequency of the scanning does affect the time averaging only if its width is smaller than the repetition frequency.