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

Journal title

International Journal of Electronics and Telecommunications




vol. 57


No 3

Publication authors

Divisions of PAS

Nauki Techniczne


International Journal of Electronics and Telecommunications (IJET, eISSN 2300-1933, untill 2013 also print ISSN 2081-8491) is a periodical of Electronics and Telecommunications Committee of Polish Academy of Sciences and it is published by Warsaw Science Publishers of PAS. It continues tradition of the Electronics and Telecommunications Quarterly (ISSN 0867-6747) established in 1955 as the Rozprawy Elektrotechniczne. The IJET is a scientific periodical where papers present the results of original, theoretical, experimental and reviewed works. They consider widely recognized aspects of modern electronics, telecommunications, microelectronics, optoelectronics, radioelectronics and medical electronics.

The authors are outstanding scientists, well‐known experienced specialists as well as young researchers – mainly candidates for a doctor's degree. The papers present original approaches to problems, interesting research results, critical estimation of theories and methods, discuss current state or progress in a given branch of technology and describe development prospects. All the papers published in IJET are reviewed by international specialists who ensure that the publications are recognized as author's scientific output.

The printed periodical is distributed among all those who deal with electronics and telecommunications in national scientific centers as well as in numeral foreign institutions, and it is subscribed by many specialists and libraries. Its electronic version is available at

The papers received are published within half a year if the cooperation between author and the editorial staff is efficient. The papers may be submitted to the editorial office by the journal web page


Polish Academy of Sciences Committee of Electronics and Telecommunications




ISSN 2081-8491 (until 2012) ; eISSN 2300-1933 (since 2013)


Hahn S. (1992), Multidimensional Complex Signals with Single-orthant Spectra, Proceedings of the IEEE, 80, 8, 1287, ; 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, ; Hitzer E. (2007), Quaternion Fourier Transform on Quaternion Fields and Generalizations, Advances in Applied Clifford Algebras, 17, 3, 497, ; 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, ; Sangwine S. (1996), Fourier Transforms of Colour Images Using Quaternion or Hypercomplex Numbers, Electronic Letters, 32, 21, 1979, ; Bülow T. (1999), Bericht Nr. 99-3. ; Ell T. (2007), Hypercomplex Fourier Transforms of Color Images, IEEE Transactions on Image Processing, 16, 1, 22, ; Alexiadis D. (2009), Estimation of Motions in Color Image Sequences Using Hypercomplex Fourier Transforms, IEEE Transactions on Image Processing, 18, 1, 168, ; Sangwine S. (2000), Color Image Filters Based on Hypercomplex Convolution, IEEE Proceedings Vision, Image & Signal Processing, 147, 2, 89, ; 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.