Multiplying an autocorrelation by an analyzing cosine yields the power spectrum.

Evidence

With a slight variation, we can use a color strip computation to get the power spectrum. The transformation starts with an autocorrelation function in the lefthand strip and a cosine of a given frequency in the middle strip. These are multiplied across row-wise as for the autocorrelation, and the result is put in the righthand strip and averaged down the third column. For a single cosine of frequency f, this gives the power spectrum at frequency f. — Eric J. Heller, Why You Hear What You Hear- An…, 406

Categorization

• DEFINE: Explains the mechanical procedure connecting autocorrelation to power spectrum via cosine multiplication.