Translations:Appendix K: Exercises/32/en

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30. Consider the effect of random noise on deconvolution. The autocorrelation of ideal random noise is zero at all lags except at zero lag. Should the effect of random noise on deconvolution operators be roughly similar to the effect of prewhitening? Both effects modify the diagonal of the autocorrelation matrix, making it more dominant. However, the noise component also slightly modifies the nonzero lags of the autocorrelation. Prewhitening is equivalent to the addition of perfect random noise to the system. Because random noise generally is already present in the system to some degree, only a minute amount of such white noise, sometimes as little as 0.1%, needs to be added to the trace for numerical stability.