D. Alfsmann, H. G. Göckler, S. J. Sangwine, and T. A. , Hypercomplex algebras in digital signal processing: Benefits and drawbacks, Signal Processing Conference, pp.1322-1326, 2007.

S. Bernstein, J. Bouchot, M. Reinhardt, and B. Heise, Generalized analytic signals in image processing: comparison, theory and applications, Quaternion and Clifford Fourier Transforms and Wavelets, pp.221-246, 2013.

F. Brackx, N. D. Schepper, and F. Sommen, The two-dimensional Clifford-Fourier transform, Journal of mathematical Imaging and Vision, vol.26, issue.1-2, pp.5-18, 2006.

E. Bedrosian, A product theorem for Hilbert transforms, 1962.
DOI : 10.1109/proc.1963.2308

S. Bernstein, The fractional monogenic signal, Hypercomplex Analysis: New Perspectives and Applications, pp.75-88, 2014.
DOI : 10.1007/978-3-319-08771-9_5

M. Bahri, E. S. Hitzer, A. Hayashi, and R. Ashino, An uncertainty principle for quaternion fourier transform, Computers & Mathematics with Applications, vol.56, issue.9, pp.2398-2410, 2008.
DOI : 10.1016/j.camwa.2008.05.032
URL : https://doi.org/10.1016/j.camwa.2008.05.032

C. P. Bridge, Introduction to the monogenic signal, 2017.

T. Bülow 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.

N. L. Bihan and S. J. Sangwine, The hyperanalytic signal, 2010.

]. F. Catoni, D. Boccaletti, R. Cannata, V. Catoni, E. Nichelatti et al., The mathematics of Minkowski space-time: with an introduction to commutative hypercomplex numbers, 2008.

F. R. Chung, Spectral graph theory, 1997.

R. R. Coifman and S. Lafon, Diffusion maps. Applied and computational harmonic analysis, vol.21, pp.5-30, 2006.

C. , Preliminary sketch of biquaternions, Proceedings of the London Mathematical Society, issue.1, pp.381-395, 1871.

R. R. Coifman, S. Lafon, A. B. Lee, M. Maggioni, B. Nadler et al., Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps, Proceedings of the, vol.102, pp.7426-7431, 2005.
DOI : 10.1073/pnas.0500334102
URL : http://www.pnas.org/content/102/21/7426.full.pdf

J. Cockle, III. on a new imaginary in algebra, Philosophical Magazine Series, vol.3, issue.226, pp.37-47, 1849.

H. De-bie, Clifford algebras, Fourier transforms, and quantum mechanics, Mathematical Methods in the Applied Sciences, vol.35, issue.18, pp.2198-2228, 2012.

H. De-bie, N. D. Schepper, and F. Sommen, The class of Clifford-Fourier transforms, Journal of Fourier Analysis and Applications, vol.17, issue.6, pp.1198-1231, 2011.

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

T. A. , Hypercomplex spectral transformations, phd dissertation, 1992.

T. A. Ell and S. J. Sangwine, Hypercomplex fourier transforms of color images, IEEE Transactions on image processing, vol.16, issue.1, pp.22-35, 2007.

M. Felsberg, T. Bülow, G. Sommer, and V. M. Chernov, Fast algorithms of hypercomplex Fourier transforms, Geometric computing with Clifford algebras, pp.231-254, 2001.
DOI : 10.1007/978-3-662-04621-0_10

J. Flamant, P. Chainais, and N. Le-bihan, Polarization spectrogram of bivariate signals, Acoustics, Speech and Signal Processing, pp.3989-3993, 2017.
DOI : 10.1109/icassp.2017.7952905
URL : https://hal.archives-ouvertes.fr/hal-01655120

M. Felsberg and G. Sommer, The monogenic signal, IEEE Transactions on Signal Processing, vol.49, issue.12, pp.3136-3144, 2001.
DOI : 10.1109/78.969520

D. Gabor, Theory of communication, Journal of the Institution of Electrical EngineersPart III: Radio and Communication Engineering, vol.93, issue.26, pp.429-441, 1946.

S. Gong and Y. Gong, Concise Complex Analysis: Revised, 2007.
DOI : 10.1142/6457

W. R. Hamilton and . Ii, on quaternions; or on a new system of imaginaries in algebra, Philosophical Magazine Series, vol.3, issue.163, pp.10-13, 1844.

X. Huo, X. Ni, and A. K. Smith, A survey of manifold-based learning methods. Recent advances in data mining of enterprise data, pp.691-745, 2007.

S. Hahn and K. Snopek, The unified theory of n-dimensional complex and hypercomplex analytic signals, Bulletin of the Polish Academy of Sciences: Technical Sciences, vol.59, issue.2, pp.167-181, 2011.

S. Hahn and K. Snopek, Quasi-analytic multidimensional signals, Bulletin of the Polish Academy of Sciences: Technical Sciences, vol.61, issue.4, pp.1017-1024, 2013.
DOI : 10.2478/bpasts-2013-0109
URL : https://content.sciendo.com/downloadpdf/journals/bpasts/61/4/article-p1017.pdf

S. L. Hahn and K. M. Snopek, Complex and Hypercomplex Analytic Signals: Theory and Applications, 2016.

P. Ketchum, Analytic functions of hypercomplex variables, Transactions of the American Mathematical Society, vol.30, issue.4, pp.641-667, 1928.
DOI : 10.2307/1989440
URL : https://www.ams.org/tran/1928-030-04/S0002-9947-1928-1501452-7/S0002-9947-1928-1501452-7.pdf

A. Y. Khrennikov and . Superanalysis, , vol.470, 2012.

K. Kodaira, Complex manifolds and deformation of complex structures, 2006.

S. G. Krantz, Function theory of several complex variables, vol.340, 2001.

S. G. Krantz, Explorations in harmonic analysis: with applications to complex function theory and the Heisenberg group, 2009.

N. and L. Bihan, Foreword to the special issue, Hypercomplex Signal Processing". Signal Processing, vol.136, pp.1-106, 2017.

N. , L. Bihan, and S. Sangwine, The H-analytic signal, 16th European Signal Processing Conference (EUSIPCO-2008), pp.8-9, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00337657

N. Le-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

J. M. Lee, Introduction to smooth manifolds, 2001.
DOI : 10.1007/978-1-4419-9982-5

B. Mawardi and E. M. Hitzer, Clifford-Fourier transformation and uncertainty principle for the Clifford geometric algebra Cl 3,0. Advances in applied Clifford algebras, vol.16, pp.41-61, 2006.

J. R. Munkres, Analysis on manifolds, 2018.

P. S. Pedersen, Cauchy's integral theorem on a finitely generated, real, commutative, and associative algebra, Advances in mathematics, vol.131, issue.2, pp.344-356, 1997.

G. Scheffers, Sur la généralisation des fonctions analytiques. CR Acad, vol.116, p.1893

, Sketching the History of Hypercomplex Numbers

S. J. Sangwine and N. Le-bihan, Hypercomplex analytic signals: extension of the analytic signal concept to complex signals, Signal Processing Conference, pp.621-624, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00170947

E. C. Titchmarsh, Introduction to the theory of Fourier integrals, vol.2, 1948.

D. Vakman, On the analytic signal, the Teager-Kaiser energy algorithm, and other methods for defining amplitude and frequency, IEEE Transactions on Signal Processing, vol.44, issue.4, pp.791-797, 1996.

M. Verbitsky, Hypercomplex structures on Kähler manifolds. Geometric & Functional Analysis GAFA, vol.15, pp.1275-1283, 2005.
DOI : 10.1007/s00039-005-0537-4
URL : http://arxiv.org/pdf/math/0406390v2.pdf

V. S. Vladimirov and I. V. Volovich, Superanalysis. I. Differential calculus. Theoretical and Mathematical Physics, vol.59, issue.1, pp.317-335, 1984.

V. S. Vladimirov and I. V. Volovich, Superanalysis. II. Integral calculus. Theoretical and Mathematical Physics, vol.60, issue.2, pp.743-765, 1984.

B. Yu and H. Zhang, The Bedrosian identity and homogeneous semi-convolution equations, J. Integral Equations Appl, vol.20, issue.4, pp.527-568, 2008.
DOI : 10.1216/jie-2008-20-4-527
URL : https://doi.org/10.1216/jie-2008-20-4-527

H. Zhang, Multidimensional analytic signals and the Bedrosian identity. Integral Equations and Operator Theory, vol.78, pp.301-321, 2014.
DOI : 10.1007/s00020-013-2120-y
URL : http://arxiv.org/pdf/1212.6602.pdf