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Article

Sangwine, Stephen J and Hitzer, Eckhard (2020) Polar decomposition of complexified quaternions and octonions. Advances in Applied Clifford Algebras, 30 (2). DOI https://doi.org/10.1007/s00006-020-1048-y

Hitzer, Eckhard and Sangwine, Stephen (2019) Foundations of Conic Conformal Geometric Algebra and Compact Versors for Rotation, Translation and Scaling. Advances in Applied Clifford Algebras, 29 (5). DOI https://doi.org/10.1007/s00006-019-1016-6

Hitzer, Eckhard and Sangwine, Stephen (2019) Construction of multivector inverse for Clifford algebras over 2m+1-dimensional vector spaces from multivector inverse for Clifford algebras over 2m-dimensional vector spaces. Advances in Applied Clifford Algebras, 29 (2). DOI https://doi.org/10.1007/s00006-019-0942-7

Yasmin, Shagufta and Sangwine, Stephen J (2018) Multi-directional colour edge detector using linear quaternion system convolution. IET Image Processing, 12 (7). pp. 1111-1116. DOI https://doi.org/10.1049/iet-ipr.2017.0921

Hitzer, Eckhard and Sangwine, Stephen (2017) Multivector and multivector matrix inverses in real Clifford algebras. Applied Mathematics and Computation, 311. pp. 375-389. DOI https://doi.org/10.1016/j.amc.2017.05.027

Fletcher, P and Sangwine, SJ (2017) The development of the quaternion wavelet transform. Signal Processing, 136. pp. 2-15. DOI https://doi.org/10.1016/j.sigpro.2016.12.025

Sangwine, Stephen J and Hitzer, Eckhard (2017) Clifford Multivector Toolbox (for MATLAB). Advances in Applied Clifford Algebras, 27 (1). pp. 539-558. DOI https://doi.org/10.1007/s00006-016-0666-x

Sangwine, Stephen J (2017) On harmonic analysis of vector-valued signals. Mathematical Methods in the Applied Sciences, 40 (1). pp. 22-30. DOI https://doi.org/10.1002/mma.3938

De Bie, H and De Schepper, N and Ell, TA and Rubrecht, K and Sangwine, SJ (2015) Connecting spatial and frequency domains for the quaternion Fourier transform. Applied Mathematics and Computation, 271. pp. 581-593. DOI https://doi.org/10.1016/j.amc.2015.09.045

Sangwine, Stephen J (2015) Comments on ‘A structure-preserving method for the quaternion LU decomposition in quaternionic quantum theory’ by Minghui Wang and Wenhao Ma. Computer Physics Communications, 188. pp. 128-130. DOI https://doi.org/10.1016/j.cpc.2014.11.016

Le Bihan, Nicolas and Sangwine, Stephen J and Ell, Todd A (2014) Instantaneous frequency and amplitude of orthocomplex modulated signals based on quaternion Fourier transform. Signal Processing, 94 (1). pp. 308-318. DOI https://doi.org/10.1016/j.sigpro.2013.06.028

Hitzer, E and Sangwine, SJ (2013) Quaternion and Clifford Fourier Transforms and Wavelets. Quaternion and Clifford Fourier Transforms and Wavelets, abs/13. pp. 1-338. DOI https://doi.org/10.1007/978-3-0348-0603-9

Sangwine, Stephen J and Ell, Todd A (2012) Complex and hypercomplex discrete Fourier transforms based on matrix exponential form of Euler’s formula. Applied Mathematics and Computation, 219 (2). pp. 644-655. DOI https://doi.org/10.1016/j.amc.2012.06.055

Sangwine, Stephen J and Ell, Todd A and Le Bihan, Nicolas (2011) Fundamental Representations and Algebraic Properties of Biquaternions or Complexified Quaternions. Advances in Applied Clifford Algebras, 21 (3). pp. 607-636. DOI https://doi.org/10.1007/s00006-010-0263-3

Sangwine, Stephen J and Alfsmann, Daniel (2010) Determination of the Biquaternion Divisors of Zero, Including the Idempotents and Nilpotents. Advances in Applied Clifford Algebras, 20 (2). pp. 401-410. DOI https://doi.org/10.1007/s00006-010-0202-3

Sangwine, Stephen J and Bihan, Nicolas Le (2010) Quaternion Polar Representation with a Complex Modulus and Complex Argument Inspired by the Cayley-Dickson Form. Advances in Applied Clifford Algebras, 20 (1). pp. 111-120. DOI https://doi.org/10.1007/s00006-008-0128-1

Said, S and Le Bihan, N and Sangwine, SJ (2008) Fast Complexified Quaternion Fourier Transform. IEEE Transactions on Signal Processing, 56 (4). pp. 1522-1531. DOI https://doi.org/10.1109/tsp.2007.910477

Ell, Todd A and Sangwine, Stephen J (2007) Quaternion involutions and anti-involutions. Computers & Mathematics with Applications, 53 (1). pp. 137-143. DOI https://doi.org/10.1016/j.camwa.2006.10.029

Book Section

Sangwine, Stephen J (2013) Perspectives on Color Image Processing by Linear Vector Methods Using Projective Geometric Transformations. In: Advances in Imaging and Electron Physics. Elsevier, pp. 283-307. ISBN 978-0-12-407670-9. Official URL: http://dx.doi.org/10.1016/b978-0-12-407670-9.00006...

Sangwine, SJ and Ell, TA and Le Bihan, N (2009) Hypercomplex models and processing of vector images. In: Multivariate Image Processing. ISTE/Wiley, pp. 407-436. ISBN 978-1-84821-139-1.

Monograph

Sangwine, Stephen and Hitzer, Eckhard (2019) Polar decomposition of complexified quaternions and octonions. Technical Report. University of Essex, School of Computer Science and Electronic Engineering. (Unpublished)

Hitzer, E and Sangwine, SJ (2016) Multivector and multivector matrix inverses in real Clifford algebras. UNSPECIFIED. CES-534, University of Essex, Colchester.

Sangwine, Stephen J (2015) Octonion associators. Working Paper. arXiv. (Unpublished)

Conference or Workshop Item

Hitzer, E and Sangwine, SJ (2013) Preface. In: UNSPECIFIED, ? - ?.

Bihan, Nicolas Le and Sangwine, Stephen J (2013) Quaternionic Spectral Analysis of Non-Stationary Improper Complex Signals. In: UNSPECIFIED, ? - ?.

Book

Ell, Todd A and Bihan, Nicolas Le and Sangwine, Stephen J (2014) Quaternion Fourier Transforms for Signal and Image Processing. Wiley, pp. 1-136. ISBN 9781848214781. Official URL: http://dx.doi.org/10.1002/9781118930908

Qadri, MY and Sangwine, SJ (2013) Multicore Technology: Architecture, Reconfiguration, and Modeling. CRC Press. ISBN 9781439880630. Official URL: http://dx.doi.org/10.1201/b15268

Hitzer, E and Sangwine, SJ (2013) Quaternion and Clifford Fourier Transforms and Wavelets. Trends in Mathematics . Springer, Basel. ISBN 978-3-0348-0602-2.

Other

Sangwine, SJ (2014) On harmonic analysis of vector-valued signals. arXiv.org.