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Published online by Cambridge University Press:  22 August 2018

Patrick Flandrin
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École normale supérieure de Lyon
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References

Scott, É.-L., “Principes de phonautographie” (sealed manuscript), Paris: Archives de l’Académie des sciences, January 26, 1857.Google Scholar
Scott, É.-L., “Inscription automatique des sons de l’air au moyen d’une oreille artificielle,” Comptes Rendus Ac. Sc. Paris, Vol. LIII, No. 3, pp. 10811, 1861.Google Scholar
Koenig, W., Dunn, H. K., and Lacy, D. Y., “The sound spectrograph,” J. Acoust. Soc. Amer., Vol. 18, No. 1, pp. 1949, 1946.CrossRefGoogle Scholar
Potter, R. K., Kopp, G. A., and Green, H. C., Visible Speech, Amsterdam: D. von Nostrand, 1947.Google Scholar
Abbott, B. P. et al., “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett., Vol. 116, No. 6, pp. 061102–1–061102–16, 2016.Google Scholar
Chassande-Mottin, É., Jaffard, S., and Meyer, Y., “Des ondelettes pour détecter les ondes gravitationnelles,” Gazette de la Société Mathématique de France, No. 148, pp. 61–4, 2016.Google Scholar
Flandrin, P., Time-Frequency/Time-Scale Analysis, San Diego, CA: Academic Press, 1999.Google Scholar
Donoho, D., “50 years of Data Science,” J. Comput. Graph. Stat., Vol. 26, No. 4, pp. 745– 66, 2017.Google Scholar
Ade, P. A. R. et al., “Planck 2013 results. I. Overview of products and scientific results,” Astron. Astrophys., Vol. 571, A1, 2014.Google Scholar
Wiener, N., Extrapolation, Interpolation, and Smoothing of Stationary Time Series, New York: John Wiley & Sons, 1949.Google Scholar
Blanc-Lapierre, A. and Fortet, R., Théorie des Fonctions Aléatoires, Paris: Masson, 1953.Google Scholar
Fourier, J., Théorie Analytique de la Chaleur, Paris: Firmon-Didot, 1822.Google Scholar
Escudié, B., Gazanhes, C., Tachoire, H., and Torra, V., Des Cordes aux Ondelettes, Aix-enProvence: Publications de l’Université de Provence, 2001.Google Scholar
Cooley, J. W. and Tukey, J. W., “An algorithm for the machine calculation of complex Fourier series,” Math. Comput., Vol. 19, pp. 297301, 1965.CrossRefGoogle Scholar
Kahane, J. P., “Fourier, un mathématicien inspiré par la physique,” Images de la Physique 2009, Article 01, CNRS, 2009. www.cnrs.fr/publications/imagesdelaphysique/couv-PDF/IdP2009/Article_01.pdfGoogle Scholar
Wiener, N., Ex-Prodigy: My Childhood and Youth, Cambridge, MA: MIT Press, 1964.Google Scholar
Grossmann, A. and Morlet, J., “Decomposition of Hardy functions into square-integrable wavelets of constant shape,” SIAM J. Math. Anal., Vol. 15, pp. 72336, 1984.Google Scholar
Meyer, Y., Ondelettes et Opérateurs I. Ondelettes, Paris: Hermann, 1990.Google Scholar
Daubechies, I., Ten Lectures on Wavelets, Philadelphia, PA: SIAM, 1992.CrossRefGoogle Scholar
Mallat, S., A Wavelet Tour of Signal Processing – The Sparse Way (3rd edn.), Burlington, MA: Academic Press, 2009.Google Scholar
Boashash, B. (ed.), Time-Frequency Signal Analysis and Processing – A Comprehensive Reference (2nd edn.), Amsterdam: Elsevier, 2016.Google Scholar
Cohen, L., Time-Frequency Analysis, Englewood Cliffs, NJ: Prentice Hall, 1995.Google Scholar
Gröchenig, K., Foundations of Time-Frequency Analysis, Boston, MA: Birkhäuser, 2011.Google Scholar
Spallanzani, L., Lettere sopra il sospetto di un nuovo senso nei pipistrelli, Torino: Nella Stamperia reale, 1794.Google Scholar
Pierce, G. W. and Griffin, D. R., “Experimental determination of supersonic notes emitted by bats,” J. Mammal., Vol. 19, pp. 4545, 1938.CrossRefGoogle Scholar
Simmons, J. A., “A view of the world through the bat’s ear: The formation of acoustic images in echolocation,” Cognition, Vol. 33, pp. 55199, 1989.CrossRefGoogle ScholarPubMed
Berry, M. V., “Hearing the music of the primes: Auditory complementarity and the siren song of zeta,” J. Phys. A: Math. Theor., Vol. 45, 382001, 2012.CrossRefGoogle Scholar
Mazur, B. and Stein, W., Prime Numbers and the Riemann Hypothesis, Cambridge: Cambridge University Press, 2016.Google Scholar
Gabor, D., “Theory of communication,” J. IEE, Vol. 93, pp. 42941, 1946.Google Scholar
Ville, J., “Théorie et applications de la notion de signal analytique,” Câbles et Transmissions, Vol. 2A, pp. 6174, 1948.Google Scholar
Chassande-Mottin, É. and Flandrin, P., “On the stationary phase approximation of chirp spectra,” in Proceedings IEEE International Symposium on Time-Frequency and Time-Scale Analysis, pp. 11720, Pittsburgh, PA: IEEE, 1998.Google Scholar
Flandrin, P., “Time frequency and chirps,” in Proceedings of SPIE 4391, Wavelet Applications VIII, 161, 2001.Google Scholar
Vakman, D., “On the analytic signal, the Teager-Kaiser energy algorithm, and other methods for defining amplitude and frequency,” IEEE Trans. Signal Proc., Vol. 44, No. 4, pp. 7917, 1996.Google Scholar
Flandrin, P., Sageloli, J., Sessarego, J. P., and Zakharia, M., “Application of time-frequency analysis to the characterization of surface waves on elastic targets,” Acoust. Lett., Vol. 10, No. 2, pp. 238, 1986.Google Scholar
Storey, L. R. O., “An investigation of whistling atmospherics,” Proc. Phil. Trans. Roy. Soc. A, Vol. 246, No. 908, pp. 11341, 1953.Google Scholar
Kevlahan, N. K.-R. and Vassilicos, J. C., “The space and scale dependencies of the self-similar structure of turbulence,” Proc. Phil. Trans. Roy. Soc. A, Vol. 447, No. 1930, pp. 34163, 1994.Google Scholar
Schiff, S. J. et al., “Brain chirps: Spectrographic signatures of epileptic seizures,” Clin. Neurophysiol., Vol. 111, No. 6, pp. 9538, 2000.CrossRefGoogle ScholarPubMed
Duchêne, J., Devedeux, D., Mansour, S., and Marque, C., “Analyzing uterine EMG: Tracking instantaneous burst frequency,” IEEE Eng. Med. Biol. Mag. Vol. 14, No. 2, pp. 12532, 1995.CrossRefGoogle Scholar
Sornette, D., “Discrete scale invariance and complex dimensions,” Phys. Rep., Vol. 297, No. 5, pp. 23970, 1998.CrossRefGoogle Scholar
Simmonds, J. and MacLennan, D., Fisheries Acoustics: Theory and Practice (2nd edn.), Oxford: Blackwell Science, 2005.Google Scholar
Goupillaud, P. L., “Signal design in the ‘vibroseis’ ® technique,” Geophysics, Vol. 41, pp. 1291304, 1976.CrossRefGoogle Scholar
Papoulis, A., Probability, Random Variables, and Stochastic Processes, New York: McGraw-Hill, 1965.Google Scholar
Vetterli, M., Kovac̆ević, J., and Goyal, V. K., Foundations of Signal Processing, Cambridge: Cambridge University Press, 2014.CrossRefGoogle Scholar
Unser, M. and Tafti, P., An Introduction to Sparse Stochastic Processes, Cambridge: Cambridge University Press, 2014.Google Scholar
Schreier, J. and Scharf, L. L., Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals, Cambridge: Cambridge University Press, 2010.CrossRefGoogle Scholar
Pugh, E. L., “The generalized analytic signal,” J. Math. Anal. Appl., Vol. 89, No. 2, pp. 67499, 1982.Google Scholar
Heideman, M. T., Johnson, D. H., and Burrus, C. S., “Gauss and the history of the Fast Fourier Transform,” IEEE Acoust. Speech Signal Proc. Mag., Vol. 1, No. 4, pp. 1421, 1984.Google Scholar
De Bruijn, N. G., “Uncertainty principles in Fourier analysis,” in Inequalities (Shisha, O., ed.), pp. 5771, New York: Academic Press, 1967.Google Scholar
Glauber, R. J., “Coherent and incoherent states of the radiation field,” Phys. Rev., Vol. 131, pp. 276688, 1963.Google Scholar
Helström, C. W., “An expansion of a signal in Gaussian elementary signals,” IEEE Trans. Inf. Theory, Vol. 12, No. 1, pp. 812, 1968.Google Scholar
Husimi, K., “Some formal properties of the density matrix,” Proc. Phys. Math. Soc. Jpn., Vol. 22, pp. 264314, 1940.Google Scholar
Heisenberg, W., “Über den anschaulichen Inhalt der quantentheoretischen Kinematic und Mechanik,” Zeit. Physik, Vol. 43, No. 3–4, pp. 17298, 1927.CrossRefGoogle Scholar
Weyl, H., Gruppentheorie und Quantenmechanik, Leipzig: S. Hirzel, 1928.Google Scholar
Schrödinger, E., “Zum Heisenbergschen Unschärfeprinzip,” Sitzungsberichte der Preussischen Akademie der Wissenschaften, Vol. 14, pp. 296303, 1930. English translation available at http://arxiv.org/abs/quant-ph/9903100.Google Scholar
Hirschman, I. I., “A note on entropy,” Amer. J. Math., Vol. 79, No. 1, pp. 1526, 1957.CrossRefGoogle Scholar
Beckner, W., “Inequalities in Fourier analysis,” Ann. Math., Vol. 102, No. 1, pp. 15982, 1975.Google Scholar
Folland, G. B. and Sitaram, A., “The uncertainty principle: A mathematical survey,” J. Fourier Anal. Appl., Vol. 3, No. 3, pp. 20738, 1997.Google Scholar
Dembo, A., Cover, T. M., and Thomas, J. A., “Information theoretic inequalities,” IEEE Trans. Inf. Theory, Vol. 37, No. 6, pp. 150118, 1991.CrossRefGoogle Scholar
Flandrin, P., “The many roads to time-frequency,” in Nonlinear and Nonstationary Signal Processing (Walden, A. et al., eds.), Isaac Newton Institute Series, pp. 27591, Cambridge: Cambridge University Press, 2001.Google Scholar
Woodward, P. M., Probability and Information Theory with Applications to Radar, London: Pergamon Press, 1953.Google Scholar
Flandrin, P., “Ambiguity functions,” in [21], Article 5.1, pp. 238–43.Google Scholar
Turin, G. L., “An introduction to matched filters,” IRE Trans. Inf. Theory, Vol. 6, No. 3, pp. 31129, 1960.Google Scholar
Wigner, E. P., “On the quantum correction for thermodynamic equilibrium,” Phys. Rev., Vol. 40, pp. 74959, 1932.Google Scholar
Hudson, R. L., “When is the Wigner quasi-probabilty density non-negative?,” Rep. Math. Phys., Vol. 6, No. 2, pp. 24952, 1974.Google Scholar
Rioul, O. and Flandrin, P., “Time-scale energy distributions: A general class extending wavelet transforms,” IEEE Trans. Acoust. Speech Signal Proc., Vol. 40, No. 7, pp. 174657, 1992.Google Scholar
Percival, D. B. and Walden, A. T., Spectral Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques, Cambridge: Cambridge University Press, 1993.CrossRefGoogle Scholar
Folland, G. B., Harmonic Analysis in Phase Space, Ann. of Math. Studies No. 122, Princeton, NJ: Princeton University Press, 1989.CrossRefGoogle Scholar
Claasen, T. A. C. M. and Mecklenbräuker, W. F. G., “The Wigner distribution – A tool for time-frequency signal analysis. Part I: Continuous-time signals, Part II: Discrete-time signals, Part III: Relations with other time-frequency signal transformations,” Philips J. Res., Vol. 35, pp. 21750, 276–300, and 372–89, 1980.Google Scholar
Mecklenbräuker, W. F. G. and Hlawatsch, F. (eds.), The Wigner Distribution: Theory and Applications in Signal Processing, Amsterdam: Elsevier, 1998.Google Scholar
Lieb, E. H., “Integral bounds for radar ambiguity functions and Wigner distributions,” J. Math. Phys., Vol. 31, pp. 5949, 1990.Google Scholar
Baraniuk, R. G., Flandrin, P., Janssen, A. J. E. M., and Michel, O. J. J., “Measuring time-frequency information content using the Rényi entropies,” IEEE Trans. Inf. Theory, Vol. 47, No. 4, pp. 1391409, 2001.Google Scholar
Flandrin, P., “Maximum signal energy concentration in a time-frequency domain,” in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing ICASSP-88, pp. 217679, New York, 1988.Google Scholar
Janssen, A. J. E. M., “Optimality property of the Gaussian window spectrogram,” IEEE Trans. Signal Proc., Vol. 39, pp. 2024, 1991.CrossRefGoogle Scholar
Flandrin, P., “Cross-terms and localization in time-frequency energy distributions,” in [21], Article 4.2, pp. 151–8.Google Scholar
Silverman, R. A., “Locally stationary random processes,” IEEE Trans. Inf. Theory, Vol. 3, pp. 1827, 1957.CrossRefGoogle Scholar
Borgnat, P., Flandrin, P., Honeine, P., Richard, C., and Xiao, J., “Testing stationarity with surrogates: A time-frequency approach,” IEEE Trans. Signal Proc., Vol. 58, No. 7, pp. 345970, 2010.CrossRefGoogle Scholar
Mandelbrot, B. B., The Fractal Geometry of Nature (3rd edn.), New York: W. H. Freeman and Co., 1983.Google Scholar
Makhoul, J., “Linear prediction: A tutorial review,” Proc. IEEE, Vol. 63, No. 4, pp. 56180.Google Scholar
Abry, P., Gonçalvès, P., and Flandrin, P., “Wavelets, spectrum analysis, and 1/ f processes,” in Wavelets and Statistics (Antoniadis, A. et al., eds.), Lecture Notes in Statistics, Vol. 103, pp. 1529, New York: Springer-Verlag, 1995.Google Scholar
Theiler, J., Eubank, S., Longtin, A., Galdrikian, B., and Farmer, J. D., “Testing for nonlinearity in time series: The method of surrogate data,” Physica D, Vol. 58, No. 1–4, pp. 7794, 1992.CrossRefGoogle Scholar
Basseville, M., “Distances measures for signal processing and pattern recognition,” Signal Proc.,Vol. 18, No. 4, pp. 34969, 1989.Google Scholar
Hlawatsch, F. and Flandrin, P., “The interference structure of the Wigner distribution and related time-frequency signal representations,” in [69], pp. 59–133.Google Scholar
Okabe, A., Boots, B., Sugihara, K., and Chiu, S. N., Spatial Tessellations: Concepts and Applications of Voronoi Diagrams (2nd edn.), New York: John Wiley & Sons, 2000.Google Scholar
Flandrin, P. and Gonçalvès, P., “Geometry of affine time-frequency distributions,” Appl. Comp. Harm. Anal., Vol. 3, No. 1, pp. 1039, 1996.Google Scholar
Kodera, K., de Villedary, C., and Gendrin, R., “A new method for the numerical analysis of non-stationary signals,” Phys. Earth Plan. Int., Vol. 12, pp. 14250, 1976.CrossRefGoogle Scholar
Kodera, K., Gendrin, R., and de Villedary, C., “Analysis of time-varying signals with small BT values,” IEEE Trans. Acoust. Speech Signal Proc., Vol. 26, pp. 6476, 1978.Google Scholar
Auger, F. and Flandrin, P., “Improving the readability of time-frequency and time-scale representations by the reassignment method,” IEEE Trans. Acoust. Speech Signal Proc., Vol. 43, No. 5, pp. 106889, 1995.Google Scholar
Flandrin, P., Auger, F., and Chassande-Mottin, É., “Time-frequency reassignment – From principles to algorithms,” in Applications in Time-Frequency Signal Processing (Papandreou-Suppappola, A., ed.), Chapter 5, pp. 179203, Boca Raton, FL: CRC Press, 2003.Google Scholar
Fulop, S. A. and Fitz, K., “A spectrogram for the twenty-first century,” Acoust. Today, Vol. 2, No. 3, pp. 2633, 2006.Google Scholar
Welch, P. D., “The use of the Fast Fourier Transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms,” IEEE Trans. Audio Electroacoust., Vol. AU-15, pp. 703, 1967.Google Scholar
Thomson, D. J., “Spectrum estimation and harmonic analysis,” Proc. IEEE, Vol. 70, No. 9, pp. 105596, 1982.CrossRefGoogle Scholar
Xiao, J. and Flandrin, P., “Multitaper time-frequency reassignment for nonstationary spectrum estimation and chirp enhancement,” IEEE Trans. Signal Proc., Vol. 55, No. 6, pp. 285160, 2007.Google Scholar
Daubechies, I. and Maes, S., “A nonlinear squeezing of the continuous wavelet transform based on auditory nerve models,” in Wavelets in Medicine and Biology (Aldroubi, A. and Unser, M., eds.), pp. 52746, Boca Raton, FL: CRC Press, 1996.Google Scholar
Auger, F., Flandrin, P., Lin, Y. T., McLaughlin, S., Meignen, S., Oberlin, T., and Wu, H. T., “Time-frequency reassignment and synchrosqueezing,” IEEE Signal Proc. Mag., Vol. 30, No. 6, pp. 3241, 2013.CrossRefGoogle Scholar
Flandrin, P., “A note on reassigned Gabor spectrograms of Hermite functions,” J. Fourier Anal. Appl., Vol. 19, No. 2, pp. 28595, 2012.Google Scholar
Flandrin, P., “Some features of time-frequency representations of multicomponent signals,” in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing ICASSP-84, pp. 41B.4.1–41B.4.4, San Diego, CA, 1984.Google Scholar
Donoho, D. L., “Compressed sensing,” IEEE Trans. Inf. Theory, Vol. 52, No. 4, pp. 1289– 306, 2006.Google Scholar
Candès, E., Romberg, J., and Tao, T., “Stable signal recovery from incomplete and inaccurate measurements,” Comm. Pure Appl. Math., Vol. 59, No. 8, pp. 120723, 2006.Google Scholar
Flandrin, P. and Borgnat, P., “Time-frequency energy distributions meet compressed sensing,” IEEE Trans. Signal Proc., Vol. 58, No. 6, pp. 297482, 2010.Google Scholar
Flandrin, P., Pustelnik, N., and Borgnat, P., “On Wigner-based sparse time-frequency distributions,” in Proceedings of IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing CAMSAP-15, Cancun, 2015.Google Scholar
Oberlin, T., Meignen, S., and Perrier, V., “Second-order synchrosqueezing transform or invertible reassignment? Towards ideal time-frequency representations,” IEEE Trans. Signal Proc., Vol. 63, No. 5, pp. 133544, 2015.Google Scholar
Pham, D. H. and Meignen, S., “High-order synchrosqueezing transform for multicomponent signals analysis – With an application to gravitational-wave signal,” IEEE Trans. Signal Proc., Vol. 65, No. 12, pp. 316878, 2017.Google Scholar
Huang, N. E. and Chen, S. P. (eds.), Hilbert-Huang Transform and Its Applications (2nd edn.), Singapore: World Scientific, 2014.Google Scholar
Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N.-C., Tung, C. C., and Liu, H. H., “The Empirical Mode Decomposition and the Hilbert Spectrum for nonlinear and nonstationary time series analysis,” Proc. Roy. Soc. A, Vol. 454, pp. 90395, 1998.Google Scholar
Daubechies, I., Lu, J., and Wu, H.-T., “Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool,” Appl. Comp. Harm. Anal., Vol. 30, No. 1, pp. 24361, 2011.Google Scholar
Rilling, G., Flandrin, P., and Gonçalves, P., “On Empirical Mode Decomposition and its algorithms,” in Proceedings of IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing NSIP-03, Grado (Italy), 2003.Google Scholar
Colominas, M., Schlotthauer, G., Torres, M. E., and Flandrin, P., “Noise-assisted EMD methods in action,” Adv. Adapt. Data Anal., Vol. 4, No. 4, pp. 1250025.1–1250025.11, 2013.Google Scholar
Chassande-Mottin, É., Daubechies, I., Auger, F., and Flandrin, P., “Differential reassignment,” IEEE Signal Proc. Lett., Vol. 4, No. 10, pp. 2934, 1997.Google Scholar
Bargmann, V., “On a Hilbert space of analytic functions and an associated integral transform,” Comm. Pure Appl. Math., Vol. 14, pp. 187214, 1961.CrossRefGoogle Scholar
Auger, F., Chassande-Mottin, É., and Flandrin, P., “On phase-magnitude relationships in the Short-Time Fourier Transform,” IEEE Signal Proc. Lett., Vol. 19, No. 5, pp. 26770, 2012.Google Scholar
Auger, F., Chassande-Mottin, É., and Flandrin, P., “Making reassignment adjustable: The Levenberg-Marquardt approach,” in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing of ICASSP-12, pp. 388992, Kyoto, 2012.Google Scholar
Hansson-Sandsten, M. and Brynolfsson, J., “The scaled reassigned spectrogram with perfect localization for estimation of Gaussian functions,” IEEE Signal Proc. Lett., Vol. 22, No. 1, pp. 1004, 2015.Google Scholar
Lim, Y., Shinn-Cunningham, B., and Gardner, T. J., “Sparse contour representation of sound,” IEEE Signal Proc. Lett., Vol. 19, No. 10, pp. 6847, 2012.CrossRefGoogle Scholar
Chassande-Mottin, É., “Méthodes de réallocation dans le plan temps-fréquence pour l’analyse et le traitement de signaux non stationnaires,” PhD thesis, Université de Cergy-Pontoise, France, 1998.Google Scholar
Gardner, T. J. and Magnasco, M. O., “Sparse time-frequency representations,” Proc. Natl. Acad. Sci., Vol. 103, No. 16, pp. 60949, 2006.Google Scholar
Meignen, S., Gardner, T., and Oberlin, T., “Time-frequency ridge analysis based on reassignment vector,” Proceedings of 23rd European Signal Processing Conference EUSIPCO-15, pp. 148690, Nice, 2015.Google Scholar
Meignen, S., Oberlin, T., Depalle, Ph., Flandrin, P., and McLaughlin, S., “Adaptive multimode signal reconstruction from time-frequency representations,” Proc. Phil. Trans. Roy. Soc. A, Vol. 374: 20150205, 2016.Google Scholar
Delprat, N., Escudié, B., Guillemain, Ph., Kronland-Martinet, R., Tchamitchian, Ph., and Torrésani, Bruno, “Asymptotic wavelet and Gabor analysis: Extraction of instantaneous frequencies,” IEEE Trans. Inf. Theory, Vol. 38, No. 2, pp. 64464, 1992.Google Scholar
Carmona, R., Hwang, W.-L., and Torrésani, B., Practical Time-Frequency Analysis: Gabor and Wavelet Transforms With an Implementation in S, San Diego, CA: Academic Press, 1998.Google Scholar
Bardenet, R., Flamant, J., and Chainais, P., “On the zeros of the spectrogram of white noise,” arXiv:1708.00082v1, 2017.Google Scholar
Flandrin, P., “On spectrogram local maxima,” in Proceedings IEEE International Conference on Acoustics, Speech and Signal Processing ICASSP-07, pp. 397983, New Orleans, 2017.Google Scholar
Conway, J. and Sloane, N. J. A., Sphere Packings, Lattices and Groups (3rd edn.), New York: Springer-Verlag, 1999.Google Scholar
Diggle, P. J., Statistical Analysis of Spatial Point Patterns (2nd edn.), London: Academic Press, 2003.Google Scholar
Stoyan, D., Kendall, W. S., and Mecke, J., Stochastic Geometry and Its Applications, New York: John Wiley & Sons, 1995.Google Scholar
Churchman, L. S., Flyvberg, H., and Spudich, J. A., “A non-Gaussian distribution quantifies distances measured with fluorescence localization techniques,” Biophys. J., Vol. 90, pp. 66871, 2006.CrossRefGoogle ScholarPubMed
Abramowitz, M. and Stegun, I., Handbook of Mathematical Functions, London: Dover, 1965.Google Scholar
Embrechts, P., Klüppelberg, C., and Mikosch, T., Modeling Extremal Events for Insurance and Finance, Berlin-Heidelberg: Springer-Verlag, 1997.CrossRefGoogle Scholar
Coles, S., An Introduction to Statistical Modeling of Extreme Values, London: Springer, 2001.Google Scholar
Calka, P., “An explicit expression for the distribution of the number of sides of the typical Poisson-Voronoi cell,” Adv. Appl. Prob., Vol. 35, pp. 86370, 2003.Google Scholar
Ferenc, J.-S. and Néda, Z., “On the size distribution of Poisson Voronoi cells,” Physica A, Vol. 385, pp. 51826, 2007.Google Scholar
Tanemura, M., “Statistical distributions of Poisson-Voronoi cells in two and three dimensions,” Forma, Vol. 18, pp. 22147, 2003.Google Scholar
Lucarini, V., “From symmetry breaking to Poisson point process in 2D – Voronoi tessellations: The generic nature of hexagons,” J. Stat. Phys., Vol. 130, pp. 104762, 2008.Google Scholar
Wang, A., “An industrial-strength audio search algorithm,” in Proceedings of Fourth International Conference on Music Information Retrieval ISMIR-03, Baltimore, MD, 2003.Google Scholar
Klimenko, S., Yakushin, I., Mercer, A., and Mitselmakher, G., “A coherent method for detection of gravitational wave bursts,” Class. Quant. Grav., Vol. 25, No. 11, pp. 114029, 2008.Google Scholar
Haenggi, M., Stochastic Geometry for Wireless Networks, Cambridge: Cambridge University Press, 2013.Google Scholar
Boas, R. P., Entire Functions, New York: Academic Press, 1954.Google Scholar
Toda, M., “Phase retrieval problem in quantum chaos and its relation to the origin of irreversibility I,” Physica D, Vol. 59, pp. 12141, 1992.CrossRefGoogle Scholar
Hough, J. B., Krishnapur, M., Peres, Y., and Virág, B., Zeros of Gaussian Analytic Functions and Determinantal Point Processes, AMS University Lecture Series, Vol. 51, 2009.Google Scholar
Lebœuf, P. and Voros, A., “Chaos-revealing multiplicative representation of quantum eigenstates,” J. Phys. A: Math. Gen., Vol. 23, pp. 176574, 1990.Google Scholar
Korsch, H. J., Müller, C., and Wiescher, H., “On the zeros of the Husimi distribution,” J. Phys. A: Math. Gen., Vol. 30, pp. L677L684, 1997.Google Scholar
Macchi, O., “The coincidence approach to stochastic point processes,” Adv. Appl. Prob., Vol 7, No. 2, pp. 83122, 1975.Google Scholar
Biscio, C. A. N. and Lavancier, F., “Quantifying repulsiveness of determinantal point processes,” Bernoulli, Vol. 22, No. 4, pp 200128, 2016.CrossRefGoogle Scholar
Lavancier, F., Møller, J., and Rubak, E., “Determinantal point process models and statistical inference,” J. Roy. Stat. Soc. B, Vol. 77, No. 4, pp. 85377, 2015.Google Scholar
Hannay, J. H., “Chaotic analytic zero points: Exact statistics for those of a random spin state,” J. Phys. A: Math. Gen., Vol. 29, pp. L101L105, 1996.Google Scholar
Nazarov, F., Sodin, M., and Volberg, A., “Transportation to random zeroes by the gradient flow,” Geom. Funct. Anal., Vol. 17, No. 3, pp. 887935, 2007.Google Scholar
Flandrin, P., “Time-frequency filtering from spectrogram zeros,” IEEE Signal Proc. Lett., Vol. 22, No. 11, pp. 213741, 2015.Google Scholar
Balasz, P., Bayer, D., Jaillet, F., and Søndergaard, P., “The pole behavior of the phase derivative of the short-time Fourier transform,” Appl. Comp. Harm. Anal., Vol. 40, pp. 61021, 2016.Google Scholar
Nye, J. F. and Berry, M. V., “Dislocations in wave trains,” Proc. Roy. Soc. Lond. A, Vol. 336, pp. 16590, 1974.Google Scholar
Blanchet, L., Damour, T., Iyer, B. R., Will, C. M., and Wiseman, A. G., “Gravitational-radiation damping of compact binary systems to second post-Newtonian order,” Phys. Rev. Lett., Vol. 74, No. 18, pp. 351518, 1995.Google Scholar
Sathyaprakash, B. S. and Dhurandhar, S. V., “Choice of filters for the detection of gravitational waves from coalescing binaries,” Phys. Rev. D, Vol. 44, pp. 381934, 1991.Google Scholar
Thorne, K. S., “Gravitational radiation,” in 300 Years of Gravitation (Hawking, S. W. and Israel, W., eds.), pp. 330458, Cambridge: Cambridge University Press, 1987.Google Scholar
Buonanno, A. and Damour, T., “Effective one-body approach to general relativistic two-body dynamics,” Phys. Rev. D, Vol. 59, pp. 084006, 1999.CrossRefGoogle Scholar
Chassande-Mottin, É. and Flandrin, P., “On the time-frequency detection of chirps,” Appl. Comp. Harm. Anal., Vol. 6, No. 2, pp. 25281, 1999.Google Scholar
Jaffard, S., Journé, J. L., and Daubechies, I., “A simple Wilson orthonormal basis with exponential decay,” SIAM J. Math. Anal., Vol. 22, pp. 55473, 1991.Google Scholar
Abbott, B. P. et al., “GW151226: Observation of gravitational waves from a 22-solar-mass binary black hole coalescence,” Phys. Rev. Lett., Vol. 116, pp. 241103–1–241103–14, 2016.Google Scholar
Flandrin, P., “The sound of silence: Recovering signals from time-frequency zeros,” in Proceedings of Asilomar Conference on Signals, Systems, and Computers, pp. 5448, Pacific Grove, CA, 2016.Google Scholar
Chassande-Mottin, É. and Flandrin, P., “On the time-frequency detection of chirps and its application to gravitational waves,” in Second Workshop on Gravitational Wave Data Analysis, pp. 4752, Paris: Éditions Frontières, 1999.Google Scholar
Nachtigall, P. E. and Moore, P. W. B. (eds.), Animal Sonar: Processes and Performance, NATO ASI Series A: Life Sciences, Vol. 156, New York: Plenum Press, 1988.Google Scholar
Nagel, T., “What is it like to be a bat?,” Phil. Rev., Vol. 83, No. 4, pp. 43550, 1974.CrossRefGoogle Scholar
Altes, R. A. and Titlebaum, E. L., “Bat signals as optimally Doppler tolerant waveforms,” J. Acoust. Soc. Amer., Vol. 48(4B), pp. 101420, 1970.Google Scholar
Simmons, J. A., “The resolution of target range by echolocating bats,” J. Acoust. Soc. Amer., Vol. 54, pp. 15773, 1973.Google Scholar
Simmons, J. A., “Perception of echo phase information in bat sonar,” Science, Vol. 207, pp. 13368, 1979.Google Scholar
Simmons, J. A., Ferragamo, M., Moss, C. F., Stevenson, S. B., and Altes, R. A., “Discrimination of jittered sonar echoes by the echolocating bat, Eptesicus fuscus: The shape of targets images in echolocation,” J. Comp. Physiol. A, Vol. 167, pp. 589616, 1990.CrossRefGoogle ScholarPubMed
Møhl, B., “Detection by a pipistrelle bat of normal and reverse replica of its sonar pulses,” Acustica, Vol. 61, pp. 7582, 1986.Google Scholar
Altes, R. A., “Some theoretical concepts for echolocation,” in [158], pp. 725–52.Google Scholar
Altes, R. A., “Detection, estimation, and classification with spectrograms,” J. Acoust. Soc. Amer., Vol. 67, No. 4, pp. 123246, 1980.Google Scholar
Altes, R. A., “Echolocation as seen from the viewpoint of radar/sonar theory,” in Localization and Orientation in Biology and Engineering (Varjú, D. and Schnitzler, H.-U., eds.), pp. 23444, Berlin: Springer-Verlag, 1984.Google Scholar
Saillant, P., Simmons, J. A., and Dear, S., “A computational model of echo processing and acoustic imaging in frequency-modulated echolocating bats: The spectrogram correlation and transformation receiver,” J. Acoust. Soc. Amer., Vol. 94, pp. 2691712, 1993.Google Scholar
Jaffard, S. and Meyer, Y., “Wavelet methods for pointwise regularity and local oscillations of functions, Memoirs Amer. Math. Soc., Vol. 123, No. 587, 1996.CrossRefGoogle Scholar
Falconer, K., Fractal Geometry, New York: John Wiley & Sons, 1990.Google Scholar
Berry, M. V. and Lewis, Z. V., “On the Weierstrass-Mandelbrot fractal function,” Proc. Roy. Soc. London A, Vol. 370, pp. 45984, 1980.Google Scholar
Borgnat, P. and Flandrin, P., “On the chirp decomposition of Weierstrass-Mandelbrot functions, and their time-frequency interpretation,” Appl. Comp. Harm. Anal., Vol. 15, pp. 13446, 2003.Google Scholar
Bertrand, J., Bertand, P., and Ovarlez, J.-Ph., “The Mellin transform,” in The Transforms and Applications Handbook (Poularikas, A., ed.), Boca Raton, FL: CRC Press, 1990.Google Scholar
Flamant, J., Le Bihan, N., and Chainais, P., “Time-frequency analysis of bivariate signals,” arXiv:1609.02463, 2016.Google Scholar
Roussel, B., Cabart, C., Fève, G., Thibierge, E., and Degiovanni, P., “Electron quantum optics as quantum signal processing,” Phys. Status Solidi B, Vol. 254, pp. 16000621, 2017.Google Scholar
Stanković, L. J., Daković, M., and Sejdić, E., “Vertex-frequency analysis: A way to localize graph spectral components,” IEEE Signal Proc. Mag., Vol. 34, No. 4, pp. 17682, 2017.Google Scholar

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