arXiv subjects

Jacob N. Oppenheim

Publications and source records attributed to Jacob N. Oppenheim.

3 recordsLinked to original sources

arXiv2013

Minimal Bounds on Nonlinearity in Auditory Processing

Time-reversal symmetry breaking is a key feature of nearly all natural sounds, caused by the physics of sound production. While attention has been paid to the response of the auditory system to "natural stimuli," very few psychophysical tests have been performed. We conduct psychophysical measurements of time-frequency acuity for both "natural" notes (sharp attack, long decay) and time-reversed ones. Our results demonstrate significantly greater precision, arising from enhanced temporal acuity, for such "natural" sounds over both their time-reversed versions and theoretically optimal gaussian pulses, without a corresponding decrease in frequency acuity. These data rule out models of auditory processing that obey a modified "uncertainty principle" between temporal and frequency acuity and suggest the existence of statistical priors for naturalistic stimuli, in the form of sharp-attack, long-decay notes. We are additionally able to calculate a minimal theoretical bound on the order of the nonlinearity present in auditory processing. We find that only matching pursuit, spectral derivatives, and reassigned spectrograms are able to satisfy this criterion.

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arXiv2013

Human Time-Frequency Acuity Beats the Fourier Uncertainty Principle

The time-frequency uncertainty principle states that the product of the temporal and frequency extents of a signal cannot be smaller than $1/(4π)$. We study human ability to simultaneously judge the frequency and the timing of a sound. Our subjects often exceeded the uncertainty limit, sometimes by more than tenfold, mostly through remarkable timing acuity. Our results establish a lower bound for the nonlinearity and complexity of the algorithms employed by our brains in parsing transient sounds, rule out simple "linear filter" models of early auditory processing, and highlight timing acuity as a central feature in auditory object processing.

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arXiv2012

A Topological Phase Transition in the Scheidegger Model of River Networks

We investigate the canonical Scheidegger Model of river network morphology for the case of convergent and divergent underlying topography, by embedding it on a cone. We find two distinct phases corresponding to few, long basins and many, short basins, respectively, separated by a singularity in number of basins, indicating a phase transition. Quantifying basin shape through Hack's Law $l\sim a^h$ gives distinct values for the exponent $h$, providing a method of testing our hypotheses. The generality of our model suggests implications for vascular morphology, in particular differing number and shapes of arterial and venous trees.

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