Summary
The so-called Wiener-Khinchine theorem, asserting the positivity of the Fourier transform of the autocorrelation function of a stationary stochastic process, is shown to hold rigorously in the context of distribution theory.
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References
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Tzanakis, C. A note on the fourier transform of a positive-definite function. Nuov Cim B 108, 339–342 (1993). https://doi.org/10.1007/BF02887493
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DOI: https://doi.org/10.1007/BF02887493