My understanding is that signal averaging works this way. If we take the average of the waveform, we get the average of the signal component (which is the magnitude of the signal) and the average of the noise component (which becomes closer to zero as number of samples are increased).
However, this is based on the assumption that the noise has zero mean and constant variance (i.e. white or Gaussian noise). What if the noise is not white? For example, what if the noise decreases as frequency increases? Will the noise still be averaged out by signal averaging?