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Time-frequency super-resolution with superlets

Author

Listed:
  • Vasile V. Moca

    (Transylvanian Institute of Neuroscience)

  • Harald Bârzan

    (Transylvanian Institute of Neuroscience
    Technical University of Cluj-Napoca)

  • Adriana Nagy-Dăbâcan

    (Transylvanian Institute of Neuroscience)

  • Raul C. Mureșan

    (Transylvanian Institute of Neuroscience)

Abstract

Due to the Heisenberg–Gabor uncertainty principle, finite oscillation transients are difficult to localize simultaneously in both time and frequency. Classical estimators, like the short-time Fourier transform or the continuous-wavelet transform optimize either temporal or frequency resolution, or find a suboptimal tradeoff. Here, we introduce a spectral estimator enabling time-frequency super-resolution, called superlet, that uses sets of wavelets with increasingly constrained bandwidth. These are combined geometrically in order to maintain the good temporal resolution of single wavelets and gain frequency resolution in upper bands. The normalization of wavelets in the set facilitates exploration of data with scale-free, fractal nature, containing oscillation packets that are self-similar across frequencies. Superlets perform well on synthetic data and brain signals recorded in humans and rodents, resolving high frequency bursts with excellent precision. Importantly, they can reveal fast transient oscillation events in single trials that may be hidden in the averaged time-frequency spectrum by other methods.

Suggested Citation

  • Vasile V. Moca & Harald Bârzan & Adriana Nagy-Dăbâcan & Raul C. Mureșan, 2021. "Time-frequency super-resolution with superlets," Nature Communications, Nature, vol. 12(1), pages 1-18, December.
    • Handle: RePEc:nat:natcom:v:12:y:2021:i:1:d:10.1038_s41467-020-20539-9
    DOI: 10.1038/s41467-020-20539-9
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    Cited by:

    1. Yu, Qiang, 2023. "A homotopy-based wavelet method for extreme large bending analysis of heterogeneous anisotropic plate with variable thickness on orthotropic foundation," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    2. Andjelka B. Kovačević & Aleksandra Nina & Luka Č. Popović & Milan Radovanović, 2022. "Two-Dimensional Correlation Analysis of Periodicity in Noisy Series: Case of VLF Signal Amplitude Variations in the Time Vicinity of an Earthquake," Mathematics, MDPI, vol. 10(22), pages 1-14, November.
    3. Woojoong Kim & Munsu Lee & Sang-Jun Park & Sung-Hyun Jang & Byeong-Su Kang & Namjin Kim & Young-Sun Hong, 2022. "An Early Fault Diagnosis Method for Ball Bearings of Electric Vehicles Based on Integrated Subband Averaging and Enhanced Kurtogram Method," Energies, MDPI, vol. 15(15), pages 1-13, July.
    4. Haoxin Zhang & Ivan Skelin & Shiting Ma & Michelle Paff & Lilit Mnatsakanyan & Michael A. Yassa & Robert T. Knight & Jack J. Lin, 2024. "Awake ripples enhance emotional memory encoding in the human brain," Nature Communications, Nature, vol. 15(1), pages 1-13, December.

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