DDF
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Here are my notes summarizing my reading of a couple related papers. The ear has a non linear transfer function which can change the inner spectrum envelope depending on external phase relationships. Doesn't mean any phase manipulation is audible, but it does mean using linear math is not really a good way to explore differences in perceived envelopes, and DBT is usually necessary.
From "Hearing, Its Psychology and Physiology" by the
Acoustical Society of America on the
audibility of 2nd harmonic distortion with a pure 370
Hz fundamental:
"The masking of an added harmonic is negligible below
a sensation level of 40 - 50 dB. From 50 to 80 dB,
the amount of harmonic necessary for an audible change
increases rapidly, first in absolute magnitude, and later
in relative magnitude as well...."
"...The qualitative character of the audible change produced
by adding this harmonic was different at the various sensation
levels of the fundamental. At low levels the harmonic was usually
heard as a separate tone. In the middle region [50 - 80 dBSPL]
it was heard as a sharpening or brightening of the timbre of the
tone, whereas at high levels the changes were so complex and so
dependent upon differences of phase that any generalization about
their character would be misleading."
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From "The representation of speech in the peripheral auditory
system", there's a paper by Schroeder and Mehgart "Auditory Masking
in the perception of speech", where they show that reversing the
phase of even one harmonics component is audible. He could even
"produce little melodies by sheer phase manipulations."
Summarizing:
Some monaural phase effects can be explained by the concept of the
inner spectrum, the spectrum available to the inner ear. This is
different than the spectrum at the outer ear due to non linearities
in the middle ear and inner ear. Identical external power spectra
can lead to substantially different inner spectra for different
phase angles.
Details:
Experiments were conducted where a 1020 Hz tone was presented and a
complex signal was used to mask the tone. The complex had a
fundamental frequency that was a submultiple of 1200 Hz and between
30 and 300 Hz. The total power spectrum of the masker was "speech
like" (1/f) and up to 6 kHz. The phase angles of the harmonics of
the masker were either constant (all equal) or random.
If the phase of the harmonics were random, the 1020 Hz had to be
greater than about 10 dB below the level of the fundamental to be
heard. As the fundamental fell below 100 Hz, the 1020 Hz had to be
louder to the point that for a 30 Hz fundamental, the 1020 Hz had to
be 2 dB louder than the fundamental. The reason is that more
harmonics were generated and these crowded around 1020 Hz.
If the phase of harmonics was constant, a very different picture
emerged. If the fundamental of the masker was above 150 Hz, the
level of the 1020 Hz had to be greater than about 4 dB below the
level of the fundamental to be heard. Below 150 Hz, the 1020 Hz
tone could be increasingly QUIETER and still be heard, to the point
that at 30 Hz, the 1020 Hz could be 38 dB below the fundamental's
level and still be heard.
The theory is that the constant phase signal has small "silent"
intervals where even a weak signal can be perceived i.e. unmasked.
This is an important distinction that is not predicted by critical
band masking theory, in fact, are actually inconsistent with
critical band masking theory.
Further convincing experiments were conducted that strongly
supported this theory.
The conclusion:
"Since speech signals have more nearly constant rather than random
phases the results reported here are believed to be relevant to the
perception of speech signals."
