Natural auditory and visual stimuli are shown to demonstrate consistent non
-Gaussian signatures: their phase-only second spectra behave approximately
as the inverse square root of frequency, a property which is due to a predo
minance of difference beats between Fourier components at slightly offset f
requencies. These second spectra also demonstrate statistical scale invaria
nce, a hypothesis which is tested explicitly by computing phase-only second
spectra from bandpass-filtered data. The bandpass frequency selectivity ob
served experimentally in sensory cells is shown to be qualitatively consist
ent with a strategy of exploiting the non-Gaussian structure of natural sig
nals.