Autocorrelations are positive-coefficient cosine sums maximal at zero lag

Evidence

Autocorrelation functions are always sums of cosines with positive coefficients. They are maximal at time t = 0, regaining their maximum at one period, if the original signal is strictlly periodic. Most functions are not autocorrelation functions—for example, the function b(t) = 2 cos(2π 100τ) – cos(2π 150τ) is not an autocorrelation. — Eric J. Heller, Why You Hear What You Hear- An…, 382

Categorization

• DEFINE: States the strong mathematical constraint that marks which functions can be autocorrelations at all.