The Wiener–Khinchin theorem says that for wide-sense stationary processes. If the Fourier transform of the autocorrelation function exists, then it equals the power spectral density. Wide-sense stationary processes require a constant mean, and an autocorrelation function only dependent on the time lag. However, when I look through proofs of Wiener–Khinchin theorem, such as https://www.comm.utoronto.ca/~frank/notes/wk.pdf it looks like they only use the autocorrelation property. So, why is a constant mean also required?
2026-03-27 07:49:09.1774597749
Why isn't a time independent autocorrelation function sufficient for Wiener–Khinchin theorem?
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