The history of applications of analytic signals in electrical and radio engineering

EUROCON 2007 - The International Conference on Computer as a Tool

Volumn , Issue , 2007, Pages 2627-2631

  Hahn, Stefan L ^a  

^a WARSAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Analytic functions; Analytic signals; Historical data

Indexed keywords

IMAGE SEGMENTATION; SPECTRUM ANALYZERS; SPEECH;

(2+1) DIMENSIONS; (2+1)-DIMENSIONAL; (E ,2E) THEORY; (MIN ,MAX ,+) FUNCTIONS; ANALYTIC FUNCTIONS; ANALYTIC SIGNALS; FOURIER SPECTRAL ANALYSIS; INTERNATIONAL CONFERENCES; PERSONAL EXPERIENCES; RADIO-ENGINEERING; SPECTRA (CO); WIGNER DISTRIBUTION (WD);

FUNCTION EVALUATION;

EID: 46149099862     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/EURCON.2007.4400463     Document Type: Conference Paper

References (29)

1. D. Gabor, "Theory of Communications," Trans. Inst. Electr. Eng., vol. 3, pp. 429-456, 1946.
2. D. Vakman, "On the analytic signal, the Teager-Kaiser energy algorithm and other methods defining the amplitude and phase," IEEE Trans. Signal Proc., vol.44, pp. 791-797, April 1996.
3. E. Bedrosian, "The Analytic Signal Representation of Modulated Waveforms," Proc. IRE, pp. 2071-2076, October 1962.
4. S. L. Hahn, Hilbert Transforms in Signal Processing, Artech House, Boston*London, 1996.
5. S. L. Hahn, "On the uniqueness of the definition of the amplitude and phase of the analytic signal," Signal Processing, vol. 83, pp. 1815-1820, 2003.
6. L. Cohen, P. Loughlin, D. Vakman, "On the ambiguity of the definition of the amplitude and phase of a signal," Signal Processing, vol. 79, pp. 301-307, 1999.
7. S. Hahn, "Complex variable frequency electric circuit theory," Proc. IEEE, vol. 52, No. 6, pp. 735-736, June 1964
8. S. L.Hahn, "Generation of random signals using interpolation functions of the sampling theory," Kleinheubacher Berichte, Deutsche Telekom, Darmstadt, Band 39, pp. 561-568, 1996.
9. H. Stark, "An extension of the Hilbert transform product theorem," Proc. IEEE, vol. 39, pp. 1359-1360, September 1971.
10. S. L. Hahn, "Complex Signals with Single-Orthant Spectra as Boundary Distributions of Multidimensional Analytic Functions," Bulletin of the Polish Academy of Sciences, Technical Sciences, vol. 51, no. 2, pp.155-161, 2003.
11. S. L. Hahn, "Multidimensional Complex Signals with Single-Orthant Spectra," Proc. IEEE, vol. 80, no. 8, pp.1287-1300, August 1992.
12. F. Peyrin, Y. M. Zhu, and R. Goutte, "Extension of the notion of analytic signals for multidimensional signals. Applications to images," in Signal Processing III: Theories and Applications, I. T. Young et al., Eds., Amsterdam, The Netherlands, pp. 677-680, 1986.
13. T. Bülow, G. Sommer, "Hypercomplex Signals - A Novel Extension of the Analytic Signal to the Multidimensional Case," IEEE Trans. Signal Proc., vol. 49, no. 11, pp. 2844-2852, November 2001.
14. S. Hahn, "The relationships of analytic and quaternionic representation of 2-D signals," Proceedings of X National Symposium of Radioscience, Poznań, Poland, 14-15 March 2002, pp. 328-332.
15. M. Felsberg, G. Sommer, "The Monogenic Signal," IEEE Trans. Signal Proc., vol. 49, no.12, pp. 3136-3144, December 2001.
16. S. L Hahn, K. M. Snopek, "Comparison of Properties of Analytic, Quaternionic and Monogenic 2D Signals," WSEAS Transactions on Computers, Issue 3, vol. 3, pp.602-611, July 2004.
17. L. Schwartz, Méthodes Mathématique pour les Science Physique, Hermann, Paris, 1965.
18. P. Antosik, J. Mikusiński, P. Sikorski, Theory of Distributions-the Sequential Approach, PWN, Warsaw, 1973.
19. S. L. Hahn, "The n-dimensional complex delta distribution," IEEE Trans. Signal Proc, vol. 44, no. 7, pp. 1833-1837, July 1996.
20. R de L. Kronig, Journal Opt. Soc. America, vol. 12, p. 547, 1926.
21. H. A. Kramers, Phys. Zeitchrift, vol. 30, p. 522, 1929.
22. M. Nieto-Vesperinas, "Dispersion relations in two dimensions. Application in the phase problem," Optik, vol. 56, no. 4, pp. 377-384, 1980.
23. M. A. Fiddy, "The Role of Analycity in Image Recovery," in Image Recovery: Theory and Applications, Edit. H. Stark, Academic Press, Orlando, Florida, Chapter 13, pp. 499-529.
24. S. L. Hahn, "The Definition of Causality of Multidimensional Signals," Kleinheubacher Berichte, Deutsche Telekom, Darmstadt, Band 45, pp. 108-110, 2002.
25. E. P. Wigner, "On the quantum correction for thermodynamic equilibrium," Phys. Rev., vol. 40, pp. 749-759, 1932.
26. J. Ville, "Théorie et application de la notion de signal analytique," Câbles et Transmission, vol. A(I), pp. 61-74, 1948.
27. B. Boashash, "Note on the use of Wigner distribution for time-frequency analysis," IEEE Trans. on Acoust., Speech. Signal Process., vol. 36, pp. 1518-1521, September 1988.
28. S. L. Hahn, "The Szilard-Wigner Distributionen von Analytischen Signalen," Kleinheubacher Berichte, Deutsche Telekom, Darmstadt, Band 42, pp.388-398, 1988.
29. S. L. Hahn, K. M. Snopek, "Wigner Distributions and Ambiguity Functions of 2D Quaternionic and Monogenic Signals," IEEE Trans. Signal Proc., vol. 53, no. 8 (Part II), pp. 311-312, August 2005.