For binary (spike train) signals, take FFT of signal or autocorrelation of signal?
For binary data (spike-trains), people use a spike-train autocovariance function (same as autocorrelation but subtracting the mean firing rate). It's commonly used to study brain oscillations (e.g. Engel &amp; Konig, 1991). There is a good description of the math in the Dayan &amp; Abbott (page 27).

Dayan, P., &amp; Abbott, L. F. (2001). Theoretical neuroscience (Vol. 806). Cambridge, MA: MIT Press.
Engel, A. K., &amp; Konig, P. (1991). Interhemispheric synchronization of oscillatory neuronal responses in cat visual cortex. Science, 252(5009), 1177.