Real short bursts have continuous spectra needing Fourier analysis, not finite cosines.

Evidence

This signal is a short burst, and the spectrum has turned out to be fairly broad and continuous. No finite set of cosines could be used to represent the autocorrelation, nor are there just a finite set of frequencies with power. This is why we needed the color strips and the Fourier analysis—to become facile with general and typical signals. — Eric J. Heller, Why You Hear What You Hear- An…, 409