Time-Frequency Analysis, Randomness and Sampling
Time-Frequency Analysis, Randomness and Sampling
José Luis Romero
(ORCID: 0000-0002-2491-8962)
Disciplines
Mathematics (100%)
Keywords
-
Irregular Sampling,
Time-Frequency Analysis,
Computational Harmonic Analysis,
Time-Frequency Localization,
Frame,
Gaussian Analytic Function
In timefrequency analysis a signal is studied simultaneously in both the time and frequency domains. For example, one-dimensional data is studied via a two-dimensional representation, called the spectrogram, that shows the evolution of the fluctuations or oscillations along space (or time). The field of time-frequency analysis is very rich, reaching into both pure and applied mathematics. Applications include audio processing, wireless communications, statistics and data analysis. The limit scale where joint time-frequency analysis is possible is given by the uncertainty principle. This project addresses a number of problems, motivated by specific applications, where the uncertainty limit is approached. Specific topics include: (a) the acquisition of signals by capturing measuring values at some locations; (b) the acquisition of signals with moving sensors; (c) the description of random processes exhibiting a repulsive behavior; (d) the numerical performance of sampling reconstruction schemes; (e) the estimation of periodicities in data that evolves with time.
Research institution(s)
Project participants
- Peter Balazs, Österreichische Akademie der Wissenschaften , associated research partner
Research Output
- 190 Citations
- 55 Publications
- 4 Datasets & models
- 2 Disseminations
- 1 Scientific Awards
- 1 Fundings
Publications
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2024
Title Hypercontractivity and strips of convergence in Hardy spaces of general Dirichlet series DOI 10.48550/arxiv.2401.09996 Type Preprint Author Carando D Link Publication -
2024
Title Random Periodic Sampling Patterns for Shift-Invariant Spaces DOI 10.1109/tit.2023.3320289 Type Journal Article Author Antezana J Journal IEEE Transactions on Information Theory -
2024
Title Estimation of Binary Time-Frequency Masks from Ambient Noise DOI 10.1137/22m149805x Type Journal Article Author Romero J Journal SIAM Journal on Mathematical Analysis Link Publication -
2024
Title Sampling in the shift-invariant space generated by the bivariate Gaussian function DOI 10.1016/j.jfa.2024.110600 Type Journal Article Author Romero J Journal Journal of Functional Analysis Link Publication -
2024
Title Normality of smooth statistics for planar determinantal point processes DOI 10.3150/23-bej1612 Type Journal Article Author Haimi A Journal Bernoulli -
2024
Title Eigenvalue estimates for Fourier concentration operators on two domains. DOI 10.1007/s00205-024-01979-9 Type Journal Article Author Marceca F Journal Archive for rational mechanics and analysis Pages 35 Link Publication -
2021
Title Spectral-norm risk rates for multi-taper estimation of Gaussian processes DOI 10.48550/arxiv.2110.06625 Type Preprint Author Romero J -
2021
Title Modelling the utility of group testing for public health surveillance DOI 10.1016/j.idm.2021.08.002 Type Journal Article Author Koliander G Journal Infectious Disease Modelling Pages 1009-1024 Link Publication -
2021
Title Efficient computation of the zeros of the Bargmann transform under additive white noise DOI 10.48550/arxiv.2108.12921 Type Preprint Author Escudero L -
2021
Title Multiple Sampling and Interpolation in Weighted Fock Spaces of Entire Functions DOI 10.1007/s11785-020-01065-4 Type Journal Article Author Escudero L Journal Complex Analysis and Operator Theory Pages 35 Link Publication -
2021
Title Sampling the Flow of a Bandlimited Function DOI 10.1007/s12220-021-00617-0 Type Journal Article Author Aldroubi A Journal The Journal of Geometric Analysis Pages 9241-9275 Link Publication -
2021
Title On dual molecules and convolution-dominated operators DOI 10.1016/j.jfa.2021.108963 Type Journal Article Author Romero J Journal Journal of Functional Analysis Pages 108963 Link Publication -
2021
Title Spectral deviation of concentration operators for the short-time Fourier transform DOI 10.48550/arxiv.2104.06150 Type Preprint Author Marceca F -
2021
Title Sign Retrieval in Shift-Invariant Spaces with Totally Positive Generator DOI 10.1007/s00041-020-09804-z Type Journal Article Author Romero J Journal Journal of Fourier Analysis and Applications Pages 27 Link Publication -
2022
Title Lipschitz Continuity of Spectra of Pseudodifferential Operators in a Weighted Sjöstrand Class and Gabor Frame Bounds DOI 10.48550/arxiv.2207.08669 Type Preprint Author Gröchenig K -
2022
Title Efficient Computation of the Zeros of the Bargmann Transform Under Additive White Noise DOI 10.1007/s10208-022-09593-5 Type Journal Article Author Escudero L Journal Foundations of Computational Mathematics Pages 279-312 Link Publication -
2022
Title Normality of smooth statistics for planar determinantal point processes DOI 10.48550/arxiv.2210.10588 Type Preprint Author Haimi A -
2022
Title Invertibility of Frame Operators on Besov-Type Decomposition Spaces DOI 10.1007/s12220-022-00887-2 Type Journal Article Author Romero J Journal The Journal of Geometric Analysis Pages 149 Link Publication -
2022
Title The planar low temperature Coulomb gas: separation and equidistribution DOI 10.4171/rmi/1340 Type Journal Article Author Ameur Y Journal Revista Matemática Iberoamericana Pages 611-648 Link Publication -
2022
Title A Differential Entropy Estimator for Training Neural Networks DOI 10.48550/arxiv.2202.06618 Type Preprint Author Pichler G -
2022
Title The density theorem for discrete series representations restricted to lattices DOI 10.1016/j.exmath.2021.10.001 Type Journal Article Author Romero J Journal Expositiones Mathematicae Pages 265-301 Link Publication -
2022
Title A multi-scale Gaussian beam parametrix for the wave equation: The Dirichlet boundary value problem DOI 10.1016/j.jde.2021.11.043 Type Journal Article Author Berra M Journal Journal of Differential Equations Pages 949-993 Link Publication -
2021
Title Coorbit spaces associated to integrably admissible dilation groups DOI 10.1007/s11854-021-0192-1 Type Journal Article Author Führ H Journal Journal d'Analyse Mathématique Pages 351-395 -
2022
Title On the existence of optimizers for time–frequency concentration problems DOI 10.1007/s00526-022-02358-6 Type Journal Article Author Nicola F Journal Calculus of Variations and Partial Differential Equations Pages 21 Link Publication -
2022
Title Comment on "Affine density, von Neumann dimension and a problem of Perelomov" DOI 10.48550/arxiv.2211.04879 Type Preprint Author Romero J -
2020
Title Multitaper Estimation on Arbitrary Domains DOI 10.1137/19m1278338 Type Journal Article Author Ande´N J Journal SIAM Journal on Imaging Sciences Pages 1565-1594 Link Publication -
2020
Title Multiple sampling and interpolation in weighted Fock spaces of entire functions DOI 10.48550/arxiv.2004.12922 Type Preprint Author Escudero L -
2020
Title Sampling the flow of a bandlimited function DOI 10.48550/arxiv.2004.14032 Type Preprint Author Aldroubi A -
2020
Title Zeros of Gaussian Weyl-Heisenberg functions and hyperuniformity of charge DOI 10.48550/arxiv.2012.12298 Type Preprint Author Haimi A -
2020
Title The density theorem for discrete series representations restricted to lattices DOI 10.48550/arxiv.2003.08347 Type Preprint Author Romero J -
2020
Title Sign retrieval in shift-invariant spaces with totally positive generator DOI 10.48550/arxiv.2005.08678 Type Preprint Author Romero J -
2023
Title Grid-Based Decimation for Wavelet Transforms with Stably Invertible Implementation DOI 10.48550/arxiv.2301.01640 Type Other Author Holighaus N Link Publication -
2023
Title Sampling in the shift-invariant space generated by the bivariate Gaussian function DOI 10.48550/arxiv.2306.13619 Type Other Author Romero J Link Publication -
2022
Title Decoupling inequalities with exponential constants DOI 10.1007/s00208-022-02418-4 Type Journal Article Author Carando D Journal Mathematische Annalen -
2022
Title Norm-controlled inversion in l^1: a support-dependent theorem and applications DOI 10.25365/thesis.73276 Type Other Author Egger S Link Publication -
2022
Title Gaussian beta ensembles: the perfect freezing transition and its characterization in terms of Beurling-Landau densities DOI 10.48550/arxiv.2205.15054 Type Preprint Author Ameur Y Link Publication -
2022
Title Improved discrepancy for the planar Coulomb gas at low temperatures DOI 10.48550/arxiv.2212.14821 Type Preprint Author Marceca F -
2021
Title On the existence of optimizers for time-frequency concentration problems DOI 10.48550/arxiv.2112.09675 Type Preprint Author Nicola F Link Publication -
2023
Title Rotated time-frequency lattices are sets of stable sampling for continuous wavelet systems DOI 10.1109/sampta59647.2023.10301410 Type Conference Proceeding Abstract Author Holighaus N Pages 1-5 -
2023
Title Grid-Based Decimation for Wavelet Transforms With Stably Invertible Implementation DOI 10.1109/taslp.2023.3235197 Type Journal Article Author Holighaus N Journal IEEE/ACM Transactions on Audio, Speech, and Language Processing -
2023
Title Spectral deviation of concentration operators for the short-time Fourier transform DOI 10.4064/sm220214-17-10 Type Journal Article Author Marceca F Journal Studia Mathematica -
2023
Title Lipschitz continuity of spectra of pseudodifferential operators in a weighted Sjöstrand class and Gabor frame bounds DOI 10.4171/jst/465 Type Journal Article Author Gröchenig K Journal Journal of Spectral Theory -
2023
Title Eigenvalue estimates for Fourier concentration operators on two domains DOI 10.48550/arxiv.2301.11685 Type Preprint Author Marceca F Link Publication -
2023
Title Rotated time-frequency lattices are sets of stable sampling for continuous wavelet systems DOI 10.48550/arxiv.2307.13481 Type Preprint Author Holighaus N Link Publication -
2023
Title Random periodic sampling patterns for shift-invariant spaces DOI 10.48550/arxiv.2305.15261 Type Other Author Antezana J Link Publication -
2022
Title Estimation of binary time-frequency masks from ambient noise DOI 10.48550/arxiv.2205.10205 Type Preprint Author Romero J -
2022
Title Spectral-norm risk rates for multi-taper estimation of Gaussian processes DOI 10.1080/10485252.2022.2071888 Type Journal Article Author Romero J Journal Journal of Nonparametric Statistics Pages 448-464 Link Publication -
2022
Title Zeros of Gaussian Weyl–Heisenberg Functions and Hyperuniformity of Charge DOI 10.1007/s10955-022-02917-3 Type Journal Article Author Haimi A Journal Journal of Statistical Physics Pages 22 Link Publication -
2022
Title Fusion of Probability Density Functions DOI 10.1109/jproc.2022.3154399 Type Journal Article Author Koliander G Journal Proceedings of the IEEE Pages 404-453 Link Publication -
2022
Title Sampling Trajectories for the Short-Time Fourier Transform DOI 10.1007/s00041-022-09977-9 Type Journal Article Author Speckbacher M Journal Journal of Fourier Analysis and Applications Pages 82 Link Publication -
2021
Title The Nyquist sampling rate for spiraling curves DOI 10.1016/j.acha.2020.01.005 Type Journal Article Author Jaming P Journal Applied and Computational Harmonic Analysis Pages 198-230 Link Publication -
2020
Title Decoupling inequalities with exponential constants DOI 10.48550/arxiv.2012.15293 Type Preprint Author Carando D Link Publication -
2020
Title On dual molecules and convolution-dominated operators DOI 10.48550/arxiv.2001.09609 Type Preprint Author Romero J -
2020
Title Balian–Low Type Theorems on Homogeneous Groups DOI 10.1007/s10476-020-0051-9 Type Journal Article Author Gröchenig K Journal Analysis Mathematica Pages 483-515 -
2020
Title The planar low temperature Coulomb gas: separation and equidistribution DOI 10.48550/arxiv.2010.10179 Type Preprint Author Ameur Y
Datasets & models
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2022
Link
Title Efficient computation of the zeros of the Bargmann transform under additive white noise. Type Computer model/algorithm Public Access Link Link -
2021
Link
Title Cryo-EM datasets for evaluating spectral density estimation DOI 10.5281/zenodo.4742575 Type Database/Collection of data Public Access Link Link -
2021
Link
Title Cryo-EM datasets for evaluating spectral density estimation DOI 10.5281/zenodo.4742574 Type Database/Collection of data Public Access Link Link -
2024
Link
Title Symbolic calculations in "Hyperuniformity and non-hyperuniformity of zeros of Gaussian Weyl-Heisenberg Functions" DOI 10.5281/zenodo.12582083 Type Computer model/algorithm Public Access Link Link
Scientific Awards
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2020
Title Membership in the Young Academy of the Austrian Academy of Sciences Type Awarded honorary membership, or a fellowship, of a learned society Level of Recognition National (any country)
Fundings
-
2022
Title Marie Curie fellowship (Diana Carbajal, fellow) Type Fellowship DOI 10.3030/101064206 Start of Funding 2022 Funder Marie Sklodowska-Curie Actions