J. Gonella, A rotary-component method for analysing meteorological and oceanographic vector time series, Deep Sea Research and Oceanographic Abstracts, vol.19, issue.12, pp.833-846, 1972.
DOI : 10.1016/0011-7471(72)90002-2

C. N. Mooers, A technique for the cross spectrum analysis of pairs of complex-valued time series, with emphasis on properties of polarized components and rotational invariants, Deep Sea Research and Oceanographic Abstracts, vol.20, issue.12, pp.1129-1141, 1973.
DOI : 10.1016/0011-7471(73)90027-2

B. I. Erkmen and J. H. Shapiro, Optical coherence theory for phase-sensitive light, SPIE Optics+ Photonics, International Society for Optics and Photonics, pp.63050-63050, 2006.

A. Ahrabian, N. U. Rehman, and D. Mandic, Bivariate Empirical Mode Decomposition for Unbalanced Real-World Signals, IEEE Signal Processing Letters, vol.20, issue.3
DOI : 10.1109/LSP.2013.2242062

J. Samson, Pure states, polarized waves, and principal components in the spectra of multiple, geophysical time-series, Geophysical Journal International, vol.72, issue.3, pp.647-664, 1983.
DOI : 10.1111/j.1365-246X.1983.tb02825.x

V. Sakkalis, Review of advanced techniques for the estimation of brain connectivity measured with eeg/meg, Computers in biology and medicine 41, pp.1110-1117, 2011.

P. J. Schreier and L. L. Scharf, Stochastic time-frequency analysis using the analytic signal: why the complementary distribution matters, IEEE Transactions on Signal Processing, vol.51, issue.12, pp.3071-3079, 2003.
DOI : 10.1109/TSP.2003.818911

P. J. Schreier and L. L. Scharf, Statistical signal processing of complex-valued data: the theory of improper and noncircular signals, 2010.
DOI : 10.1017/CBO9780511815911

B. Picinbono and P. Bondon, Second-order statistics of complex signals, IEEE Transactions on Signal Processing, vol.45, issue.2, 1997.
DOI : 10.1109/78.554305

P. Amblard, M. Gaeta, and J. Lacoume, Statistics for complex variables and signals ??? Part I: Variables, Signal Processing, vol.53, issue.1, pp.1-13, 1996.
DOI : 10.1016/0165-1684(96)00071-0

P. Amblard, M. Gaeta, and J. Lacoume, Statistics for complex variables and signals ??? Part II: signals, Signal Processing, vol.53, issue.1, pp.15-25, 1996.
DOI : 10.1016/0165-1684(96)00072-2

S. Olhede and A. Walden, Polarization phase relationships via multiple Morse wavelets. II. Data analysis, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.459, issue.2031, pp.641-657, 2003.
DOI : 10.1098/rspa.2002.1050

P. J. Schreier, Polarization Ellipse Analysis of Nonstationary Random Signals, IEEE Transactions on Signal Processing, vol.56, issue.9, 2008.
DOI : 10.1109/TSP.2008.925961

A. T. Walden, Rotary components, random ellipses and polarization: a statistical perspective, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.110, issue.1, 1984.
DOI : 10.1093/biomet/82.1.201

A. Serroukh and A. T. Walden, Wavelet scale analysisof bivariate time series ii:statistical properties for linear processes, Journal of Nonparametric Statistics, vol.13, issue.1, pp.37-56, 2000.
DOI : 10.1093/biomet/82.3.619

P. Rubin-delanchy and A. T. Walden, Kinematics of Complex-Valued Time Series, IEEE Transactions on Signal Processing, vol.56, issue.9, pp.4189-4198, 2008.
DOI : 10.1109/TSP.2008.926106

T. Tanaka and D. P. Mandic, Complex Empirical Mode Decomposition, IEEE Signal Processing Letters, vol.14, issue.2, pp.101-104, 2007.
DOI : 10.1109/LSP.2006.882107

G. Rilling, P. Flandrin, P. Goncalves, and J. M. Lilly, Bivariate Empirical Mode Decomposition, IEEE Signal Processing Letters, vol.14, issue.12, pp.936-939, 2007.
DOI : 10.1109/LSP.2007.904710
URL : https://hal.archives-ouvertes.fr/inria-00570563

J. M. Lilly and S. C. Olhede, Bivariate Instantaneous Frequency and Bandwidth, IEEE Transactions on Signal Processing, vol.58, issue.2, pp.591-603, 2010.
DOI : 10.1109/TSP.2009.2031729

J. M. Lilly and S. C. Olhede, Analysis of Modulated Multivariate Oscillations, IEEE Transactions on Signal Processing, vol.60, issue.2
DOI : 10.1109/TSP.2011.2173681

D. Gabor, Theory of communication, Journal of the Institution of Electrical Engineers - Part I: General, vol.94, issue.73, pp.429-457, 1946.
DOI : 10.1049/ji-1.1947.0015

J. Ville, Théorie et applications de la notion de signal analytique, Cables et Transmission, vol.2, pp.61-74, 1948.

J. H. Conway and D. A. Smith, On quaternions and octonions: their geometry, arithmetic, and symmetry, 2003.

T. Bulow and G. Sommer, Hypercomplex signals-a novel extension of the analytic signal to the multidimensional case, IEEE Transactions on Signal Processing, vol.49, issue.11, pp.2844-2852, 2001.
DOI : 10.1109/78.960432

S. L. Altmann, Rotations, quaternions, and double groups, Courier Corporation, 2005.

T. A. Ell, N. Le-bihan, and S. J. Sangwine, Quaternion Fourier transforms for signal and image processing, 2014.
DOI : 10.1002/9781118930908
URL : https://hal.archives-ouvertes.fr/hal-00987367

J. E. Jamison, Extension of some theorems of complex functional analysis to linear spaces over the quaternions and Cayley numbers, 1970.

S. Mallat, A wavelet tour of signal processing: the sparse way, Academic press, 2008.

O. Teichmüller, Operatoren im wachsschen raum, Journal für die reine und angewandte Mathematik, pp.73-124, 1936.

P. Flandrin, Time-frequency/time-scale analysis Academic press, 1998.

B. Picinbono, On instantaneous amplitude and phase of signals, IEEE Transactions on Signal Processing, vol.45, issue.3, 1997.
DOI : 10.1109/78.558469

B. Boashash, Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals, Proceedings of the IEEE, pp.520-538, 1992.
DOI : 10.1109/5.135376

N. , L. Bihan, S. J. Sangwine, and T. A. , Instantaneous frequency and amplitude of orthocomplex modulated signals based on quaternion fourier transform, Signal Processing, vol.94, pp.308-318, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00939866

S. J. Sangwine and N. L. Bihan, Quaternion Polar Representation with a Complex Modulus and Complex Argument Inspired by the Cayley-Dickson Form, Advances in applied Clifford algebras, pp.111-120, 2010.
DOI : 10.1007/s00006-008-0128-1
URL : https://hal.archives-ouvertes.fr/hal-00515650

M. Born and E. Wolf, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light, CUP Archive, 2000.
DOI : 10.1017/CBO9781139644181

N. Delprat, B. Escudié, P. Guillemain, R. Kronland-martinet, P. Tchamitchian et al., Asymptotic wavelet and Gabor analysis: extraction of instantaneous frequencies, IEEE Transactions on Information Theory, vol.38, issue.2
DOI : 10.1109/18.119728
URL : https://hal.archives-ouvertes.fr/hal-01222729

J. M. Lilly and S. C. Olhede, On the Analytic Wavelet Transform, IEEE Transactions on Information Theory, vol.56, issue.8, pp.4135-4156, 2010.
DOI : 10.1109/TIT.2010.2050935

R. A. Carmona, W. L. Hwang, and B. Torrésani, Characterization of signals by the ridges of their wavelet transforms, IEEE Transactions on Signal Processing, vol.45, issue.10, pp.2586-2590, 1997.
DOI : 10.1109/78.640725
URL : https://hal.archives-ouvertes.fr/hal-01223134

R. A. Carmona, W. L. Hwang, and B. Torrésani, Multiridge detection and time-frequency reconstruction, IEEE Transactions on Signal Processing, vol.47, issue.2, pp.480-492, 1999.
DOI : 10.1109/78.740131
URL : https://hal.archives-ouvertes.fr/hal-01223139

A. M. Sykulski, S. C. Olhede, and J. M. Lilly, An improper complex autoregressive process of order one, arXiv preprint

J. M. Lilly and J. Park, Multiwavelet spectral and polarization analyses of seismic records, Geophysical Journal International, vol.122, issue.3, pp.1001-1021, 1995.
DOI : 10.1111/j.1365-246X.1995.tb06852.x

J. M. Lilly and R. B. Dingle, JLab: A data analysis package for Matlab, v. 1.6 Asymptotic expansions, derivation and interpretation, 1973.