Mellin transform

Transforms and Applications Handbook, Third Edition

Volumn , Issue , 2010, Pages 12-1-12-38

  Bertrand, Jacqueline ^a   Bertrand, Pierre ^b   Ovarlez, Jean Philippe ^b  

^a CNRS   (France)

^b ONERA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84863627555     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1201/9781420066531     Document Type: Chapter

References (51)

1. Titchmarsh, E. C., 1975. Introduction to the Theory of Fourier Integrals, Clarendon Press, Oxford, U.K.
2. Elfving, G., 1981. The History of Mathematics in Finland 1828-1918, Frenckell, Helsinki, Finland (ISBN 951-653-098-2).
3. Vilenkin, N. Ya., 1968. Special Functions, and the Theory of Group Representations, American Mathematical Society, Providence, RI.
4. Reid, C. E. and Passin, T. B., 1992. Signal Processing in C, John Wiley & Sons, New York.
5. Marichev, O. I., 1982. Handbook of Integral Transforms of Higher Transcendental Functions: Theory, and Algorithmic Tables, Ellis Horwood Ltd., Chichester, U.K.
6. Flajolet, P., Gourdon, X., and Dumas, P., 1995. Mellin transforms, and asymptotics: Harmonic sums, Theoret. Comput. Sci., 144, 3-58.
7. Zemanian, A. H., 1987. Generalized Integral Transformations, Dover Publications, New York.
8. Misra, O. P. and Lavoine, J. L., 1986. Transform Analysis of Generalized Functions, North-Holland Mathematics Studies, Vol. 119, Elsevier, Amsterdam, the Netherlands.
9. Bleistein, N. and Handelsman, R. A., 1986. Asymptotic Expansions of Integrals, Dover Publications, New York.
10. Kang, F., 1958. Generalized Mellin transforms I, Sc. Sinica, 7, 582-605.
11. Gelfand, I. M. and Shilov, G. E., 1964. Generalized Functions, Vol. 1, Academic Press, Inc., New York.
12. Patterson, S. J., 1989. An Introduction to the Theory of the Riemann Zeta-Function, Cambridge University Press, Cambridge, U.K.
13. Edwards, H. M., 1974. Riemann’s Zeta Function, Academic Press, New York.
14. Ditkin, V. A. and Prudnikov, A. P., 1965. Integral Transforms, and Operational Calculus, Pergamon Press, Oxford, New York.
15. Prudnikov, A. P., Brychkov, Yu, A., and Marichev, O. I., 1990. Integrals, and Series, Vol. 3: More Special Functions, Gordon, and Breach, New York.
16. Oberhettinger, F., 1974. Tables of Mellin Transforms, Springer-Verlag, New York.
17. Gradshteyn, I. S. and Ryzhik, I. M., 1994. Table of Integrals, Series, and Products, A. Jeffrey (Ed.), 5th edn., Academic Press, New York.
18. Davies, B., 1984. Integral Transforms, and their Applications, 2nd edn., Springer-Verlag, New York.
19. Sasiela, R. J., 1994. Electromagnetic Wave Propagation in Turbulence - Evaluation, and Application of Mellin Transforms, Springer series on Wave Phenomena, Vol. 18, Springer-Verlag, New York.
20. Doetsch, G., 1943. Laplace Transformation, Dover Publications, New York.
21. De Bruijn, N. G., Knuth, D. E., and Rice, S. O., 1972. The average height of planted plane trees, in Graph Theory, and Computing, R.C. Read (Ed.), Academic Press, New York.
22. Vitter, J. S. and Flajolet, P., 1990. Average-case analysis of algorithms, and data structures, in Handbook of Theoretical Computer Science, Vol. A: Algorithms, and Complexity, J. van Leeuwen (Ed.), Chapter 9, Elsevier, Amsterdam, the Netherlands.
23. Bellman, R., 1980. Analytic Number Theory, An Introduction, Benjamin-Cunnings, Reading, MA.
24. Moses, H. E. and Quesada, A. F., 1974. The power spectrum of the Mellin transformation with applications to scaling of physical quantities, J. Math. Phys., 15(6), 748-752.
25. Bertrand, J., Bertrand, P., and Ovarlez, J.P., 1990. Discrete Mellin transform for signal analysis, Proc. IEEE-ICASSP, Albuquerque, NM.
26. Bertero, M., 1992. Sampling theory, resolution limits, and inversion methods, in Inverse Problems in Scattering, and Imaging, M. Bertero, and E. R. Pike (Eds.), Malvern Physics Series, Adam Hilger, Bristol.
27. Bertrand, J., Bertrand, P., and Ovarlez, J. P., 1991. Dimensionalized wavelet transform with application to radar imaging, Proc. IEEE-ICASSP, Toronto, Ontario, Canada.
28. Klauder, J., 1980. In Functional Integration: Theory, and Applications, J. P. Antoine, and E. Tirapegui (Eds.), Plenum Press, New York.
29. Ovarlez, J. P., 1992. La Transformation de Mellin: un Outil pour l’Analyse des Signaux à Large-Bande, Doctoral thesis, University Paris 6, Paris.
30. Bertrand, J. and Bertrand, P., 1984. Représentations tempsfréquence des signaux, C.R. Acad. Sci. Paris, 299, 635-638.
31. Bertrand, J. and Bertrand, P., 1992. Affine time-frequency distributions, in Time-Frequency Signal Analysis-Methods, and Applications, B. Boashash (Ed.), Chapter V, Longman-Cheshire, Australia.
32. Bertrand, J. and Bertrand, P., 1992. A class of affine Wigner functions with extended covariance properties, J. Math. Phys., 33 (7), 2515-2527.
33. Altes, R.A., 1990. Wide-band, proportional-bandwidth Wigner-Ville analysis, IEEE Trans. Acoust., Speech, Signal Process., 38, 1005-1012.
34. Eichmann, G. and Marinovich, N. M., 1984. Scale invariant Wigner distribution, and ambiguity functions, Proc. Int. Soc. Opt. Eng. SPIE, 519, 18-24.
35. Marinovich, N. M., 1986. The Wigner distribution, and the ambiguity function: Generalizations, enhancement, compression, and some applications, PhD thesis, City University of New York, New York.
36. Cohen, L., 1993. The scale representation, IEEE Trans. Signal Process., 41(12), 3275-3292.
37. Hlawatsch, F., Papandreou, A., and Boudreaux-Bartels, F. G., 1993. Hyperbolic Class, IEEE Trans. Signal Process., 41(12), 3425-3444.
38. Ovarlez, J. P., 1993. Cramer-Rao bound computation for velocity estimation in the broad band case using the Mellin transform, Proc. IEEE-ICASSP, Minneapolis, MN.
39. Altes, R. A., 1978. The Fourier-Mellin transform, and mammalian hearing, J. Acoust. Soc. Am., 63, 174-183.
40. Zwicke, P. E. and Kiss, I., Jr., March 1983. A new implementation of the Mellin transform, and its application to radar classification of ships, IEEE Trans. Pattern Anal. Mach. Intell., 5(2), 191-199.
41. Casasent, D. and Psaltis, S., May 1978. Position, rotation, and scale invariant optical correlation, Appl. Opt., 17, 1559-1561.
42. Deformation invariant, space-variant optical pattern recognition, in Progress in Optics XVI, E. Wolf (Ed.), pp. 291-355, North-Holland, Amsterdam, the Netherlands.
43. Sheng, Y. and Arsenault, H. H., 1986. Experiments on pattern recognition using invariant Fourier-Mellin descriptors, J. Opt. Soc. Am., 3(6), 771-884.
44. Sheng, Y. and Duvernoy, J., 1986. Circular-Fourier-radial-Mellin transform descriptors for pattern recognition, J. Opt. Soc. Am., 3(6), 885-887.
45. Casasent, D. and Psaltis, S., 1977. New optical transforms for pattern recognition, Proc. IEEE, 5, 77-84.
46. Woodward, P. M., 1953. Probability, and Information Theory with Applications to Radar, Pergamon Press, New York.
47. Kelly, E. J. and Wishner, R. P., 1965. Matched filter theory for high velocity accelerating targets, IEEE Trans. Military Elect., Mil 9, 56-69.
48. Van Trees, H. L., 1971. Detection, Estimation, and Modulation Theory, Parts I, II and III, John Wiley & Sons, New York.
49. Bertrand, J., Bertrand, P., and Overlez, J. P., 1993. The wavelet approach in radar imaging, and its physical interpretation, in Progress in Wavelet Analysis, and Applications, Y. Meyer, and S. Roques (Eds.), Editions Frontières, Gif-sur-yvette, France.
50. Bertrand, J., Bertrand, P., and Ovarlez, J. P., 1994. Frequency directivity scanning in laboratory radar imaging, Int. J. Imaging Sys. Technol., 5, 39-51.
51. Ovarlez, J. P., Bertrand, J., and Bertrand, P., 1992. Computation of affine time-frequency distributions using the fast Mellin transform, Proc. IEEE-ICASSP, San Francisco, CA.