Averaged products of different-frequency cosines vanish, so only matching frequencies survive

Evidence

The CAT theorem allows us to compare two cosines by multiplying them together and averaging. If they have different frequencies, the result will be zero. The product of two cosines of the same frequency (and phase) looks like figure 4.3. If the frequencies differ, we get something like figure 4.4. which averages to zero. — Eric J. Heller, Why You Hear What You Hear- An…, 375

Categorization

• DEFINE: States the cosine averaging theorem: orthogonal cosines average to zero, only same-frequency ones survive averaging.
• XREF: This is the orthogonality of sinusoids — same mechanism behind Fourier analysis and why different partials don’t interfere in autocorrelation.