A survey of properties of ambiguity functions of analytic, quaternionic and monogenic signals

• Autorzy: Hahn G.
• Języki publikacji: EN

Abstrakty

EN

The paper investigates the properties of ambiguity functions of 2-D analytic, quaternionic and monogenic signals. In the introduction the notions of the above signals and their Wigner distributions and ambiguity functions are recalled. The properties of the ambiguity functions are investigated using two kinds of test signals: A band-pass test signal in the form of a sum of two harmonic signals with a Gaussian envelope and a low-pass signal in the form of the analytic, quaternionic and monogenic signals with a real part of a Gaussian signal of the same form as the Gaussian 2-D probability density function of correlated random variables.

Słowa kluczowe

EN

4-D Wigner distributions and ambiguity functions; 2-D analytic; quaternionic and monogenic signals

PL

funkcja niejednoznaczna 4-wymiarowego rozkładu Wignera; sygnał kwaternionowy i monogeniczny

• Wydawca: Instytut Telekomunikacji i Informatyki Uniwersytetu Technologiczno-Przyrodniczego w Bydgoszczy
• Czasopismo: Image Processing & Communications
• Rocznik: 2005
• Tom: Vol. 10, no 1
• Strony: 13--33
• Opis fizyczny: Bibliogr. 14 poz., rys.

Twórcy

autor

Hahn G.

Bibliografia

• [1] P. M. Woodward: Information theory and design of radar receivers, Proceedings of the Institute of Radio Engineers, 1951, 40, pp.1521-1524.
• [2] E. P. Wigner: On the quantum correction for thermodynamic equilibrium, Phys. Rev., vol. 40, pp. 749-752, 1932.
• [3] S. L. Hahn: Multidimensional complex signals with single-orthant spectra, Proc. IEEE, vol. 80, No. 8, Aug. 1992, pp. 1287-1300.
• [4] S. L. Hahn: Hilbert Transforms in Signal Processing, Artech House, 1996.
• [5] T. Bulow: Hypercomplex spectral signal representation for the processing and analysis of images, Bericht Nr. 9903, Institut fr Informatik und Praktische Mathematik, Christian- Albrechts-Universitt Kiel, Aug. 1999.
• [6] T. Bulow,G. Sommer: The Hypercomplex Signal - A Novel Extension of the Analytic Signal to the Multidimensional Case, IEEE Trans. Signal Processing, vol. 49, No. 11, pp. 2844-2852, Nov. 2001.
• [7] M. Felsberg: Low-Level Image Processing with the Structure Multivector, Institute of Computer Science and Applied Mathematics, Christian-Albrechts-University of Kiel, Report No. 0203, 2002.
• [8] M. Felsberg,G. Sommer : The Monogenie Signal,TEE'E Trans. Signal Processing, vol.49, No. 12, pp. 3136-3140, Dec. 2001.
• [9] G. Sommer (Ed.): Geometric Computing with Clifford Algebra, Theoretical Foundations and Applications in Computer Vision and Robotics. ISBN 3-540-41198-4, Springer Verlag Berlin Heidelberg 2001.
• [10] K. G. Larkin,D. Bone,M. A. Oldfield: Natural demodulation of two-dimensional fringe patters: I. General background of the spiral phase quadrature transform, J. Opt. Soc. Am., vol.18, No.8, pp.1862-1870, Aug. 2001.
• [11] S. L. Hahn: A review of methods of timefrequency analysis with extension for signal plane- frequency plane analysis, Kleinheubacher Berichte, Band 44, pp. 163-182, 2001.
• [12] S. L. Hahn: The theory of time-frequency distributions with extension for twodimensional signals, Metrology and Measurements Systems, Vol. VIII, No. 2, pp. 113-143, 2000.
• [13] S. L. Hahn,K. M. Snopek: Wigner Distributions and Ambiguity Functions in Image Analysis, Computer Analysis of Images and Patterns edited by W. Skarbek, Springer Verlag, pp. 537-546, 2001.
• [14] S. L. Hahn,K. M. Snopek: Wigner distributions and ambiguity functions of 2-D Quaternionic and monogenic signals, IEEE Trans, on Signal Processing, vol. 53, no. 8, August 2005 (in print).