Title

The New Insight into the Theory of 2-D Complex and Quaternion Analytic Signals

Journal title

International Journal of Electronics and Telecommunications

Yearbook

2011

Volume

vol. 57

Issue

No 3

Authors

Snopek, Kajetana

Divisions of PAS

Nauki Techniczne

Publisher

Polish Academy of Sciences Committee of Electronics and Telecommunications

Date

2011

Identifier

DOI: 10.2478/v10177-011-0038-3 ; eISSN 2300-1933 (since 2013) ; ISSN 2081-8491 (until 2012)

Source

International Journal of Electronics and Telecommunications; 2011; vol. 57; No 3

References

Hahn S. (1992), Multidimensional Complex Signals with Single-orthant Spectra, Proceedings of the IEEE, 80, 8, 1287, doi.org/10.1109/5.158601 ; Hahn S. (1996), Hilbert Transforms in Signal Processing. ; Bülow T. (2001), The Hypercomplex Signal-A Novel Extension of the Analytic Signal to the Multidimensional Case, IEEE Transactions on Signal Processing, 49, 11, 2844, doi.org/10.1109/78.960432 ; Hitzer E. (2007), Quaternion Fourier Transform on Quaternion Fields and Generalizations, Advances in Applied Clifford Algebras, 17, 3, 497, doi.org/10.1007/s00006-007-0037-8 ; T. A. Ell, "Hypercomplex Spectral Transforms," Ph.D. dissertation, University of Minnesota, Minneapolis, 1992. ; Pei S.-C. (2001), Efficient Implementation of Quaternion Fourier Transform, Convolution, and Correlation by 2-D Complex FFT, The IEEE Transactions on Signal Processing, 49, 11, 2783, doi.org/10.1109/78.960426 ; Sangwine S. (1996), Fourier Transforms of Colour Images Using Quaternion or Hypercomplex Numbers, Electronic Letters, 32, 21, 1979, doi.org/10.1049/el:19961331 ; Bülow T. (1999), Bericht Nr. 99-3. ; Ell T. (2007), Hypercomplex Fourier Transforms of Color Images, IEEE Transactions on Image Processing, 16, 1, 22, doi.org/10.1109/TIP.2006.884955 ; Alexiadis D. (2009), Estimation of Motions in Color Image Sequences Using Hypercomplex Fourier Transforms, IEEE Transactions on Image Processing, 18, 1, 168, doi.org/10.1109/TIP.2008.2007603 ; Sangwine S. (2000), Color Image Filters Based on Hypercomplex Convolution, IEEE Proceedings Vision, Image & Signal Processing, 147, 2, 89, doi.org/10.1049/ip-vis:20000211 ; Schütte H.-D. (1990), Hypercomplex Numbers in Digital Signal Processing, null, 2, 1557. ; Sercov V. (1999), Digital Hypercomplex Allpass Filters: A Novel Filters Bank Building Block, null, 181. ; Alfsmann D. (2005), Design of Hypercomplex Allpass-Based Paraunitary Filter Banks Applying Reduced Biquaternions, null, 92. ; Alfsmann D. (2007), Hypercomplex Algebras in Digital Signal Processing: Benefits and Drawbacks, null, 1322. ; Sangwine S. (2010), Fundamental Representations and Algebraic Properties of Biquaternions or Complexified Quaternions, Advances in Applied Clifford Algebras, 1. ; Snopek K. (2009), New Hypercomplex Analytic Signals and Fourier Transforms in Cayley-Dickson Algebras, Electronics and Telecommunications Quarterly, 55, 3, 403.