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bioRxiv · 10.1101/583732

Superlets: time-frequency super-resolution using wavelet sets

Moca, V. V.·Nagy-Dabacan, A.·Barzan, H.·Muresan, R. C.
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Abstract

Time-frequency analysis is ubiquitous in many fields of science. Due to the Heisenberg-Gabor uncertainty principle, a single measurement cannot estimate precisely the location of a finite oscillation in both time and frequency. Classical spectral estimators, like the short-time Fourier transform (STFT) or the continuous-wavelet transform (CWT) optimize either temporal or frequency resolution, or find a tradeoff that is suboptimal in both dimensions. Following concepts from optical super-resolution, we introduce a new spectral estimator enabling time-frequency super-resolution. Sets of wavelets with increasing bandwidth are combined geometrically in a superlet to maintain the good temporal resolution of wavelets and gain frequency resolution in the upper bands. Superlets outperform the STFT, CWT, and other super-resolution methods on synthetic data and brain signals recorded in humans and rodents, resolving time-frequency details with unprecedented precision. Importantly, superlets can reveal transient oscillation events that are hidden in the averaged time-frequency spectrum by other methods.

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Moca, V. V., Nagy-Dabacan, A., Barzan, H., Muresan, R. C.. 2019-03-21. Superlets: time-frequency super-resolution using wavelet sets. https://doi.org/10.1101/583732

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