Perceptual Coherence : Hearing and Seeing

Phase Relationships and Power Laws
Characteristics of Auditory and Visual Scenes 119
Natural visual scenes contain edges and lines that are object boundaries or
arise from occluding objects, while natural auditory scenes contain intermittent
impulse sounds along with several simultaneous ongoing complex
harmonic and inharmonic sounds. These edges, lines, and impulses cannot
be represented by simple correlations because they arise due to the phase
relationships among the Fourier components. For example, if we have a
continuous set of frequency components, those components will create a
click sound or a visual edge if they are in phase (start at the same point in
the wave) but will create a noisy static-like sound or a homogeneous texture
if they are out of phase.
The phase relationships are critical for vision. Thomson (1999) found
that natural visual scenes do have higher-order statistical structure due to
localized nonperiodic features such as bars, lines, or contours at different
positions in the scene. If the phase relationships are maintained but the amplitudes
of the components are randomized, the image is still recognizable.
But if we remove the phase information, the image comes to resemble
noise. It is likely that the formation of such edges is due to the higherfrequency
spatial components because it seems improbable that the lowfrequency
components could simultaneously be in phase with multiple
edges in a scene.
Now consider a “square” wave sound constructed by summing in phase
one sine wave representing the fundamental frequency, with additional sine
waves representing the odd harmonics. The amplitudes of the odd harmonics
are inversely proportional to their number (e.g., fundamental/1 + 3rd
harmonic/3 + 5th harmonic/5 + 7th harmonic/7 and so on). Each additional
harmonic further squares off the wave. If the harmonics composing the
square wave are not in phase, the resulting pressure wave no longer looks
like a square wave. The pressure wave still obviously repeats and the period
of the wave is still the same, being based on the fundamental frequency. In
most instances, listeners report that the in-phase and out-of-phase square
waves have the same pitch. However, the timbre or sound quality does
seem to change between the two, because the intensity of one or two of the
harmonics may have been increased due to the linear summation of the outof-phase
harmonics.
The ear has been described as being phase-deaf because the pitch does
not change. The simplest explanation is that the ear performs a frequency
analysis and encodes each frequency separately. The phase relationships
among the frequencies are lost, and pitch and timbre become based on the
amplitudes of the harmonics. But the discrimination of pitch for nonchanging
sounds is only one aspect of hearing, and is, in my opinion, not a very
important one. Phase differences do affect the formation of auditory objects.