Humans have 200 million light receptors in their eyes, 10 to 20 million
receptors devoted to smell, but only 8,000 dedicated to sound. Yet
despite this miniscule number, the auditory system is the fastest of
the five senses. Researchers credit this discrepancy to a series of
lightning-fast calculations in the brain that translate minimal input
into maximal understanding. And whatever those calculations are,
they’re far more precise than any sound-analysis program that exists
today.
In a recent issue of the Proceedings of the National
Academy of Sciences, Marcelo Magnasco, professor and head of the
Mathematical Physics Laboratory at Rockefeller University, has
published a paper that may prove to be a sound-analysis breakthrough,
featuring a mathematical method or "algorithm" that’s far more nuanced
at transforming sound into a visual representation than current
methods. "This outperforms everything in the market as a general method
of sound analysis," Magnasco says. In fact, he notes, it may be the
same type of method the brain actually uses.
former Rockefeller graduate student who is now a Burroughs Wellcome
Fund fellow at MIT, to figure out how to get computers to process
complex, rapidly changing sounds the same way the brain does. They
struck upon a mathematical method that reassigned a sound’s rate and
frequency data into a set of points that they could make into a
histogram – a visual, two-dimensional map of how a sound’s individual
frequencies move in time. When they tested their technique against
other sound-analysis programs, they found that it gave them a much
greater ability to tease out the sound they were interested in from the
noise that surrounded it.
One fundamental observation enabled
this vast improvement: They were able to visualize the areas in which
there was no sound at all. The two researchers used white noise –
hissing similar to what you might hear on an un-tuned FM radio –
because it’s the most complex sound available, with exactly the same
amount of energy at all frequency levels. When they plugged their
algorithm into a computer, it reassigned each tone and plotted the data
points on a graph in which the x-axis was time and the y-axis was
frequency. The resulting histograms showed thin, froth-like images,
each "bubble" encircling a blue spot. Each blue spot indicated a zero,
or a moment during which there was no sound at a particular frequency.
"There is a theorem," Magnasco says, "that tells us that we can know
what the sound was by knowing when there was no sound." In other words,
their pictures were being determined not by where there was volume, but
where there was silence.
"If you want to show that your analysis
is a valid signal estimation method, you have to understand what a
sound looks like when it’s embedded in noise," Magnasco says. So he
added a constant tone beneath the white noise. That tone appeared in
their histograms as a thin yellow band, bubble edges converging in a
horizontal line that cut straight through the center of the froth.
This, he says, proves that their algorithm is a viable method of
analysis, and one that may be related to how the mammalian brain parses
sound.
"The applications are immense, and can be used in most
fields of science and technology," Magnasco says. And those
applications aren’t limited to sound, either. It can be used for any
kind of data in which a series of time points are juxtaposed with
discrete frequencies that are important to pick up. Radar and sonar
both depend on this kind of time-frequency analysis, as does
speech-recognition software. Medical tests such as
electroencephalograms (EEGs), which measure multiple, discrete
brainwaves use it, too. Geologists use time-frequency data to determine
the composition of the ground under a surveyor’s feet, and an angler’s
fishfinder uses the method to determine the water’s depth and locate
schools of fish. But current methods are far from exact, so the
algorithm has plenty of potential opportunities. "If we were able to do
extremely high-resolution time-frequency analysis, we’d get
unbelievable amounts of information from technologies like radar,"
Magnasco says. "With radar now, for instance, you’d be able to tell
there was a helicopter. With this algorithm, you’d be able to pick out
each one of its blades." With this algorithm, researchers could one day
give computers the same acuity as human ears, and give cochlear
implants the power of 8,000 hair cells.
Source: The Rockefeller University. July 2006.