Studies in astronomical time series analysis. II  Statistical aspects of spectral analysis of unevenly spaced data Scargle, J. D.
 The power at a given frequency as computed by a periodigram (FFT is a specific case of the periodigram) of a gaussian white noise source with uniform variance is exponentially distributed: $P_z(z) = P(x<Z<z+dz) = e^{z}dz$
 The corresponding CDF: $1 e^{z}$ or $P(Z>z) = e^{z}$ which gives the probability of a large observed power at a given freq.
 If you need to average N samples, then $P(Z>z) = 1  (1e^{z})^N$ where $Z = max_n Pow(\omega_n)$
 Means of improving detection using a periodogram:
 Average in time  this means that N above will be smaller, hence a spectral peak becomes more significant.
 Cannot average too much  at some point, averaging will start to attenuate the signal!
 Decrease the number of frequencies inspected.
 Deals a good bit with nonperiodic sampling, which i guess is more common in astronomical data (the experimenter may not take a photo every day, or the same time every day (clouds!).
