Abstract Surface recordings of alpha waves are compared with narrow-band Gaussian random noise and the two are found to be indistinguishable. The three bases of comparison are the time domain, the frequency domain, and the probability density functions. Using the mathematical description of narrow-band noise, the complex demodulation technique for the detection of the alpha-wave envelope is developed and an analog computer circuit for its implementation is presented. The envelope is shown to have a Rayleigh probability density function that is completely specified by one parameter, σ x . This parameter, which is a function of time, since the EEG is a nonstationary process, should be used to summarize alpha-wave amplitude information.