Alex Berrian

For my Ph.D. dissertation, I studied reassignment methods for time-frequency analysis, which are nonlinear transformations used to obtain concentrated, precise information in the time-frequency domain.  I combined these methods with a novel type of chirplet transform to create a new, signal-adaptive transform that can sharply represent signals with fast-varying instantaneous frequencies, and that showed more impressive results with noisy signals than existing methods.  I also proved the theoretical accuracy of these methods in the non-noisy case, and ran sample experiments on synthetic and real-world bioacoustic data to demonstrate their effectiveness.

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Why reassignment methods?  For linear transformations like Fourier or wavelet transforms, the Fourier uncertainty principle causes a tradeoff between time precision and frequency precision: the more precise information you want in time, the less precise the frequency information becomes, and vice-versa.  The nonlinearity of reassignment methods circumvents this uncertainty principle, and allows a representation that is simultaneously precise in time and frequency.  In audio for instance, this is useful for determining the precise times at which a sound starts and ends, together with its fundamental frequencies.  As another example, in the medical field it may be useful for determining precisely when a patient has entered the REM sleep stage.

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Why chirplet transforms?  Fourier transforms are optimal for representing sinusoids of constant frequency, but in many real-world signals, sinusoidal components have time-varying frequencies.  A couple of examples are vocal glissandos in music, or many animal calls in the wild.  Chirplet transforms are useful for deblurring the Fourier transform of nonstationary sinusoid signals, including instances when the signal is contaminated with noise.