The power spectrum is the Fourier cosine transform of the autocorrelation

Evidence

With the preceding discussion as pretext, the so-called Wiener-Khinchin theorem will come as little surprise: it states that the power spectrum and the autocorrelation are obtainable from one another; specifically, the power spectrum is the Fourier cosine transform of the autocorrelation function. — Eric J. Heller, Why You Hear What You Hear- An…, 410

Categorization

• DEFINE: State the Wiener-Khinchin theorem’s precise content connecting autocorrelation and power spectrum.
• QUESTION: For a why-audition answer, the useful follow-up: what does it mean for perception that the ear can effectively compute this transform?
• corroborated: 2 independent passages support this claim — Eric J. Heller, Why You Hear What You Hear- An…, 410
• XREF: connects to: A signal’s autocorrelation is a cosine sum over its sinusoidal partials.; The power spectrum is blind to the relative phase of a sound’s components; Autocorrelation measures periodic self-similarity in a signal across time delays. — Eric J. Heller, Why You Hear What You Hear- An…, 369 (+1 more)

Broader Connections

• The power spectrum is blind to the relative phase of a sound’s components #expands (0.90)
• Autocorrelation measures periodic self-similarity in a signal across time delays. #complicates (0.75) — Eric J. Heller, Why You Hear What You Hear- An…, 369