Quasi-analytic multidimensional signals

• Autorzy: Hahn S. L. , Snopek K. M.
• Języki publikacji: EN

Abstrakty

EN

In a recent paper, the authors have presented the unified theory of n-dimensional (n-D) complex and hypercomplex analytic signals with single-orthant spectra. This paper describes a specific form of these signals called quasi-analytic. A quasi-analytic signal is a product of a n-D low-pass (base-band) real (in general non-separable) signal and a n-D complex or hypercomplex carrier. By a suitable choice of the carrier frequency, the spectrum of a low-pass signal is shifted into a single orthant of the Fourier frequency space with a negligible leakage into other orthants. A measure of this leakage is defined. Properties of quasi-analytic signals are studied. Problems of polar representation of quasi-analytic signals and of its lower rank representation are discussed.

Słowa kluczowe

EN

analytic complex and hypercomplex signals; polar representation; modulation techniques; lower rank signals

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2013
• Tom: Vol. 61, nr 4
• Strony: 1017--1024
• Opis fizyczny: Bibliogr. 14 poz., rys., tab.

Twórcy

autor

Hahn S. L.

• Institute of Radioelectronics, Warsaw University of Technology, 15/19 Nowowiejska St., 00-665 Warsaw, Poland

autor

Snopek K. M.

• Institute of Radioelectronics, Warsaw University of Technology, 15/19 Nowowiejska St., 00-665 Warsaw, Poland

Bibliografia

• [1] K.M. Snopek and S.L. Hahn, “The unified theory of ndimensional complex and hypercomplex analytic signals”, Bull. Polish Ac.: Tech. 59 (2), 167-181 (2011).
• [2] S.J. Sangwine and N. Le Bihan, Hypercomplex Analytic Signals: Extension of the Analytic Signal Concept to Complex Signals, EUSIPCO, Poznań, 2007.
• [3] C. Wachinger, T. Klein, and N. Navab, “The 2D analytic signal for envelope detection and feature extraction on ultrasound images”, Medical Image Analysis 16, 1073-1084 (2012).
• [4] T. B¨ulow and G. Sommer, A Novel Approach to the 2D Analytic Signal, pp. 25-32, Springer Verlag Berlin, 1999.
• [5] T. B¨ulow and G. Sommer, “The hypercomplex signal - a novel extension of the analytic signal to the multidimensional case”, IEEE Trans. Signal Processing 49 (11), 2844-2852 (2001).
• [6] S.L. Hahn, “Multidimensional complex signals with singleorthant spectra”, Proc. IEEE 80 (8), 1287-1300 (1992).
• [7] S.L. Hahn, Hilbert Transforms in Signal Processing, Artech House Inc., London, 1996.
• [8] S. Hahn, “Hilbert Transforms” in The Transforms and Applications Handbook, CRC Press, Orlando, 2010.
• [9] C. H¨ohne, R. Boehm, and J. Prager, “Application of 2- dimensional analytic signals with single-orthant spectra for processing of SAFT-reconstructed images”, in Multidim. Syst. Sign. Process., Springer Science+Business Media, New York, 2013.
• [10] S.J. Sangwine, C.J. Evans, and T.A. Ell, “Colour-sensitive edge detection using hypercomplex filters”, Proc. 10thEur. Signal Processing Conf. EUSIPCO 1, 107-110 (2000).
• [11] D S. Alexiadis and G.D. Sergiadis, “Estimation of motions in color image sequences using hypercomplex Fourier transforms”, IEEE Trans. Image Processing 18 (1), 168-187 (2009).
• [12] T. Bulow, M. Felsberg, and G. Sommer, “Non-commutative hypercomplex Fourier transforms of multidimensional signals” in Geometric Computing with Clifford Algebras, ed. G. Sommer, pp. 187-207, Springer, Berlin, 2001.
• [13] T.A. Ell and S.J. Sangwine, “Hypercomplex Fourier transforms of color images”, IEEE Trans. Image Process, 16 (1), 22-35, (2007).
• [14] S.L. Hahn and K.M. Snopek, “Comparison of properties of analytic, quaternionic and monogenic 2-D signals”, WSEAS Transactions on Computers 3 (3), 602-611 (2004). 1024