Concepedia

Fourier Analysis

Fourier Analysis is a branch of mathematical analysis that studies the representation of functions or distributions as superpositions of basic oscillatory components, typically via Fourier series and Fourier transforms, and the associated convergence, regularity, and inversion properties that underpin the spectral treatment of linear operators in mathematical physics.

15.6K

Publications

1M

Citations

20.6K

Authors

4.3K

Institutions

Publications per year

2017–2026

1.7K

Parents

Children

Publications

15.6K

The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis

Norden E. Huang, Steven Long, Man‐Li C. Wu et al. · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 1998 · 23.3K citations · Full text

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Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information

Emmanuel J. Candès, Justin Romberg, Terence Tao · IEEE Transactions on Information Theory · 2006 · 15.8K citations

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An algorithm for the machine calculation of complex Fourier series

J.W. Cooley, John W. Tukey · Mathematics of Computation · 1965 · 12.2K citations

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The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms

P. D. Welch · IEEE Transactions on Audio and Electroacoustics · 1967 · 12K citations

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Real and Complex Analysis.

G. A. Garreau, Walter Rudin · Journal of the Royal Statistical Society Series D (The Statistician) · 1987 · 11K citations

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1–5 of 15.6K

Authors

20.6K

  1. HM
    Haldun M. Özaktaş

    Bilkent University, Türkiye

    49 publications · 6.6K citations

    32

    h-index

  2. SP
    Soo‐Chang Pei

    National Taiwan University, Taiwan

    46 publications · 3.3K citations

    27

    h-index

  3. MU
    Michaël Unser

    École Polytechnique Fédérale de Lausanne, Switzerland

    26 publications · 3.7K citations

    24

    h-index

  4. TQ
    Tao Qian

    University of Macau, Macao SAR China

    39 publications · 1.6K citations

    24

    h-index

  5. JP
    John P. Boyd

    University of Michigan, United States

    34 publications · 1.7K citations

    24

    h-index

1–5 of 20.6K

Institutions

4.3K

  1. Massachusetts Institute of Technology

    Cambridge, United States

    63 h-index

    250 publications

    35.3K citations

  2. Centre National de la Recherche Scientifique

    Paris, France

    53 h-index

    509 publications

    24.9K citations

  3. Stanford University

    Stanford, United States

    51 h-index

    148 publications

    46K citations

  4. Princeton University

    Princeton, United States

    47 h-index

    140 publications

    17.2K citations

  5. University of Illinois Urbana-Champaign

    Urbana, United States

    43 h-index

    165 publications

    8.6K citations

  6. University of Michigan

    Ann Arbor, United States

    42 h-index

    160 publications

    18.5K citations

  7. École Polytechnique Fédérale de Lausanne

    Lausanne, Switzerland

    42 h-index

    177 publications

    17.1K citations

  8. California Institute of Technology

    Pasadena, United States

    42 h-index

    156 publications

    49.3K citations

1–8 of 4.3K

Venues

  1. IEEE Transactions on Signal Processing

    479 publications · 64.3K citations

    100

    h-index

  2. 61

    h-index

  3. Transactions of the American Mathematical Society

    TRAN · 244 publications · 16.1K citations

    56

    h-index

  4. Journal of the Optical Society of America A

    213 publications · 15.4K citations

    56

    h-index

  5. IEEE Transactions on Information Theory

    129 publications · 32.5K citations

    51

    h-index

1–5