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Emad, Here's
something else to consider for your research. Traditionally,
it has been dogma that the cochlea responds only to a sound?s amplitude
spectrum; therefore we should not hear changes caused by varying
phase. Yet it has been shown repeatedly that we do hear changes in
sounds as their phase spectrum is varied. How can this be? Let's
look at the problem: In terms of spectral analysis, we find that as we vary
the phase the amplitude spectrum is invariant. Therefore, we conclude that
the perceived changes in the sound are associated with changes in the phase
spectrum. Somehow, the ear must be responding to a supposedly irrelevant phase
spectrum. But where is the evidence? Here?s
an idea: If we look at the signal's waveform, we notice that its pattern also
varies in accord with the phase variations. Thus, it would appear that in lieu
of a phase analyzer, the ear "reads" waveforms. As absurd as this might seem,
how else could the sound changes be heard? We are thus convinced that the
cochlea must be processing a phase/waveform source. Now we
ask, ?What is the most available and usable _expression_ of
waveform?? Spatial
patterns can be described in terms of their inflection points, in our case,
having time-space locations identified by sequences of real and complex
zeros, readily obtained physically by finding the waveform derivatives. (H.
Voelker and A. Requicha) By using delay lines to preserve past events for
present use (the cochlea?), meaningful temporal patterns in the stream of
zeros (pitch?) can be recognized. Information such as amplitude and
direction of arrival can be associated with patterns of events that are
referenced to the zeros. In simple terms; the ear processes sound in the
time domain, not the frequency domain. The trick is to find out how the ear does
these things. And keep in mind that they are done in real time and are
synchronized with the signal waveform. So,
there you are: The most likely answer for you, that I can see, is that the
cochlea and its various parts must derive meaningful information
from signal waveforms by recognizing patterns in the temporal sequences
of their zeros. John
Bates From: emad
burke
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