Autocorrelation and power spectrum are Fourier transforms of each other via the Wiener-Khinchin theorem.

Evidence

Autocorrelation leads directly to the power spectrum. Autocorrelation is a function of time, power is a function of frequency; the two are each other’s Fourier transform. This is the Wiener-Khinchin theorem, which we motivate but do not prove here. — Eric J. Heller, Why You Hear What You Hear- An…, 358

Categorization

• DEFINE: Names and states the Wiener-Khinchin theorem relating autocorrelation time series to power spectra.