References
- ALIAN, A. A. and PHOTOPLETHYSMOGRAPHY, K. H. S. (2014). Bailliere’s Best Pract. Res., Clin. Anaesthesiol. 28 395–406.
- AUGER, F. and FLANDRIN, P. (1995). Improving the readability of time-frequency and time-scale representations by the reassignment method. IEEE Trans. Signal Process. 43 1068–1089.
- BAXLEY, R. J., WALKENHORST, B. T. and ACOSTA-MARUM, G. (2010). Complex Gaussian ratio distribution with applications for error rate calculation in fading channels with imperfect CSI. In IEEE Global Communications Conference.
-
Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. J. Roy. Statist. Soc. Ser. B 57 289–300.
- MathSciNet: MR1325392
-
BERNSTEIN, D. S. (2009). Matrix Mathematics: Theory, Facts, and Formulas, 2nd ed. Princeton Univ. Press, Princeton, NJ.
- Digital Object Identifier: 10.1515/9781400833344
- Google Scholar: Lookup Link
- MathSciNet: MR2513751
-
BROCKWELL, P. J. (2001). Continuous-time ARMA processes. In Stochastic Processes: Theory and Methods. Handbook of Statist. 19 249–276. North-Holland, Amsterdam.
- Digital Object Identifier: 10.1016/S0169-7161(01)19011-5
- Google Scholar: Lookup Link
- MathSciNet: MR1861726
-
BROCKWELL, P. J. and DAVIS, R. A. (2016). Introduction to Time Series and Forecasting, 3rd ed. Springer Texts in Statistics. Springer, Cham.
- Digital Object Identifier: 10.1007/978-3-319-29854-2
- Google Scholar: Lookup Link
- MathSciNet: MR3526245
-
CANDÈS, E. J., CHARLTON, P. R. and HELGASON, H. (2008). Detecting highly oscillatory signals by chirplet path pursuit. Appl. Comput. Harmon. Anal. 24 14–40.
- Digital Object Identifier: 10.1016/j.acha.2007.04.003
- Google Scholar: Lookup Link
- MathSciNet: MR2379113
- CHASSANDE-MOTTIN, E., FLANDRIN, P. and AUGER, F. (1998). On the statistics of spectrogram reassignment vectors. Multidimens. Syst. Signal Process. 9 355–362.
-
CHEN, Y.-C., CHENG, M.-Y. and WU, H.-T. (2014). Non-parametric and adaptive modelling of dynamic periodicity and trend with heteroscedastic and dependent errors. J. R. Stat. Soc. Ser. B. Stat. Methodol. 76 651–682.
- Digital Object Identifier: 10.1111/rssb.12039
- Google Scholar: Lookup Link
- MathSciNet: MR3210732
-
CHEN, Z. and WU, H.-T. (2021). Disentangling modes with crossover instantaneous frequencies by synchrosqueezed chirplet transforms, from theory to application. Appl. Comput. Harmon. Anal. 62 84–122.
- Digital Object Identifier: 10.1016/j.acha.2022.08.004
- Google Scholar: Lookup Link
-
Daubechies, I. (1992). Ten Lectures on Wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics 61. SIAM, Philadelphia, PA.
- Digital Object Identifier: 10.1137/1.9781611970104
- Google Scholar: Lookup Link
- MathSciNet: MR1162107
-
DAUBECHIES, I., LU, J. and WU, H.-T. (2011). Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool. Appl. Comput. Harmon. Anal. 30 243–261.
- Digital Object Identifier: 10.1016/j.acha.2010.08.002
- Google Scholar: Lookup Link
- MathSciNet: MR2754779
-
DAUBECHIES, I., WANG, Y. and WU, H. (2016). ConceFT: Concentration of frequency and time via a multitapered synchrosqueezed transform. Philos. Trans. R. Soc. Lond. Ser. A, Math. Phys. Sci. 374 20150193, 19.
- Digital Object Identifier: 10.1098/rsta.2015.0193
- Google Scholar: Lookup Link
- MathSciNet: MR3479895
-
FAN, J. and YAO, Q. (2003). Nonlinear Time Series: Nonparametric and Parametric Methods. Springer Series in Statistics. Springer, New York.
- Digital Object Identifier: 10.1007/b97702
- Google Scholar: Lookup Link
- MathSciNet: MR1964455
-
FLANDRIN, P. (1999). Time-Frequency/Time-Scale Analysis. Wavelet Analysis and Its Applications 10. Academic Press, San Diego, CA.
- MathSciNet: MR1681043
- GABOR, D. (1946). Theory of communication. Part 1: The analysis of information. J. Inst. Electr. Eng., 3 93 429–441.
-
GEL’FAND, I. M. and VILENKIN, N. YA. (1964). Generalized Functions. Vol. 4: Applications of Harmonic Analysis. Academic Press, New York.
- MathSciNet: MR0173945
-
HALLIN, M. (1978). Mixed autoregressive-moving average multivariate processes with time-dependent coefficients. J. Multivariate Anal. 8 567–572.
- Digital Object Identifier: 10.1016/0047-259X(78)90034-9
- Google Scholar: Lookup Link
- MathSciNet: MR0520964
-
HAMILTON, J. D. (1994). Time Series Analysis. Princeton Univ. Press, Princeton, NJ.
- MathSciNet: MR1278033
-
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. (1998). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 454 903–995.
- Digital Object Identifier: 10.1098/rspa.1998.0193
- Google Scholar: Lookup Link
- MathSciNet: MR1631591
- HUANG, Z., ZHANG, J., ZHAO, T. and SUN, Y. (2015). Synchrosqueezing s-transform and its application in seismic spectral decomposition. IEEE Trans. Geosci. Remote Sens. PP(99) 1–9.
- KODERA, K., VILLEDARY, C. D. and GENDRIN, R. (1976). A new method for the numerical analysis of non-stationary signals. Phys. Earth Planet. Inter. 12 142–150.
-
KORALOV, L. B. and SINAI, Y. G. (2007). Theory of Probability and Random Processes, 2nd ed. Universitext. Springer, Berlin.
- Digital Object Identifier: 10.1007/978-3-540-68829-7
- Google Scholar: Lookup Link
- MathSciNet: MR2343262
- KREUTZ-DELGADO, K. (2009). The complex gradient operator and the -calculus. ArXiv e-prints.
- LEBEDEV, N. N. and SILVERMAN, R. A. (1972). Special Functions & Their Applications. Dover Books on Mathematics, Dover.
-
LIN, C.-Y., SU, L. and WU, H.-T. (2018). Wave-shape function analysis: When cepstrum meets time-frequency analysis. J. Fourier Anal. Appl. 24 451–505.
- Digital Object Identifier: 10.1007/s00041-017-9523-0
- Google Scholar: Lookup Link
- MathSciNet: MR3776331
-
OBERLIN, T., MEIGNEN, S. and PERRIER, V. (2015). Second-order synchrosqueezing transform or invertible reassignment? Towards ideal time-frequency representations. IEEE Trans. Signal Process. 63 1335–1344.
- Digital Object Identifier: 10.1109/TSP.2015.2391077
- Google Scholar: Lookup Link
- MathSciNet: MR3312176
-
PHAM-GIA, T., TURKKAN, N. and MARCHAND, E. (2006). Density of the ratio of two normal random variables and applications. Comm. Statist. Theory Methods 35 1569–1591.
- Digital Object Identifier: 10.1080/03610920600683689
- Google Scholar: Lookup Link
- MathSciNet: MR2328495
- PICINBONO, B. (1997). On instantaneous amplitude and phase of signals. IEEE Trans. Signal Process. 45 552–560.
- PRIESTLEY, M. (1967). Power spectral analysis of non-stationary random processes. J. Sound Vib. 6 86–97.
-
PRIESTLEY, M. B. (1981). Spectral Analysis and Time Series. Vol. 1. Probability and Mathematical Statistics. Academic Press, London-New York.
- MathSciNet: MR0628735
-
Rosenblatt, M. (1956). A central limit theorem and a strong mixing condition. Proc. Natl. Acad. Sci. USA 42 43–47.
- Digital Object Identifier: 10.1073/pnas.42.1.43
- Google Scholar: Lookup Link
- MathSciNet: MR0074711
-
SCHREIER, P. J. and SCHARF, L. L. (2010). Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals. Cambridge Univ. Press, Cambridge.
- Digital Object Identifier: 10.1017/CBO9780511815911
- Google Scholar: Lookup Link
- MathSciNet: MR2769061
- SOURISSEAU, M., WU, H.-T and ZHOU, Z. (2022). Supplement to “Asymptotic analysis of synchrosqueezing transform—toward statistical inference with nonlinear-type time-frequency analysis.” https://doi.org/10.1214/22-AOS2203SUPP
- THAKUR, G., BREVDO, E., FUCKAR, N. S. and WU, H.-T. (2013). The synchrosqueezing algorithm for time-varying spectral analysis: Robustness properties and new paleoclimate applications. Signal Process. 93 1079–1094.
-
THAKUR, G. and WU, H.-T. (2011). Synchrosqueezing-based recovery of instantaneous frequency from nonuniform samples. SIAM J. Math. Anal. 43 2078–2095.
- Digital Object Identifier: 10.1137/100798818
- Google Scholar: Lookup Link
- MathSciNet: MR2837495
-
WU, H. (2013). Instantaneous frequency and wave shape functions (I). Appl. Comput. Harmon. Anal. 35 181–199.
- Digital Object Identifier: 10.1016/j.acha.2012.08.008
- Google Scholar: Lookup Link
- MathSciNet: MR3062471
- WU, H.-T. (2020). Current state of nonlinear-type time–frequency analysis and applications to high-frequency biomedical signals. Curr. Opin. Syst. Biol. 23 8–21.
-
Wu, W. B. (2005). Nonlinear system theory: Another look at dependence. Proc. Natl. Acad. Sci. USA 102 14150–14154.
- Digital Object Identifier: 10.1073/pnas.0506715102
- Google Scholar: Lookup Link
- MathSciNet: MR2172215
-
XIAO, H. and WU, W. B. (2012). Covariance matrix estimation for stationary time series. Ann. Statist. 40 466–493.
- Digital Object Identifier: 10.1214/11-AOS967
- Google Scholar: Lookup Link
- MathSciNet: MR3014314
-
XIAO, J. and FLANDRIN, P. (2007). Multitaper time-frequency reassignment for nonstationary spectrum estimation and chirp enhancement. IEEE Trans. Signal Process. 55 2851–2860.
- Digital Object Identifier: 10.1109/TSP.2007.893961
- Google Scholar: Lookup Link
- MathSciNet: MR2473558
-
YANG, H. (2015). Synchrosqueezed wave packet transforms and diffeomorphism based spectral analysis for 1D general mode decompositions. Appl. Comput. Harmon. Anal. 39 33–66.
- Digital Object Identifier: 10.1016/j.acha.2014.08.004
- Google Scholar: Lookup Link
- MathSciNet: MR3343801
-
YANG, H. (2018). Statistical analysis of synchrosqueezed transforms. Appl. Comput. Harmon. Anal. 45 526–550.
- Digital Object Identifier: 10.1016/j.acha.2017.01.001
- Google Scholar: Lookup Link
- MathSciNet: MR3842645
-
YANG, J. and ZHOU, Z. (2022). Spectral inference under complex temporal dynamics. J. Amer. Statist. Assoc. 117 133–155.
- Digital Object Identifier: 10.1080/01621459.2020.1764365
- Google Scholar: Lookup Link
- MathSciNet: MR4399075
-
Zhou, Z. (2013). Heteroscedasticity and autocorrelation robust structural change detection. J. Amer. Statist. Assoc. 108 726–740.
- Digital Object Identifier: 10.1080/01621459.2013.787184
- Google Scholar: Lookup Link
- MathSciNet: MR3174655
- zbMATH: 06195974