Rotation invariant ambiguity functions
HTML articles powered by AMS MathViewer
- by Qingtang Jiang
- Proc. Amer. Math. Soc. 126 (1998), 561-567
- DOI: https://doi.org/10.1090/S0002-9939-98-04197-5
- PDF | Request permission
Abstract:
Let $W(\psi ; x, y)$ be the wideband ambiguity function. It is obtained in this note that $y^{-\frac {\alpha +2}2}W(\psi ; x, y) (\alpha >-1)$ is $SO(2)$-invariant if and only if the Fourier transform of $\psi$ is a Laguerre function.References
- L. Auslander, T. Kailath, and S. Mitter (eds.), Signal processing. Part I, The IMA Volumes in Mathematics and its Applications, vol. 22, Springer-Verlag, New York, 1990. Signal processing theory. MR 1044592
- Ingrid Daubechies, Ten lectures on wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 61, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992. MR 1162107, DOI 10.1137/1.9781611970104
- Ingrid Daubechies, John R. Klauder, and Thierry Paul, Wiener measures for path integrals with affine kinematic variables, J. Math. Phys. 28 (1987), no. 1, 85–102. MR 870104, DOI 10.1063/1.527812
- D. Gabor, Theory of communication, J. Inst. Electr. Eng., 93(1964), 429-457.
- A. Grossmann and J. Morlet, Decomposition of Hardy functions into square integrable wavelets of constant shape, SIAM J. Math. Anal. 15 (1984), no. 4, 723–736. MR 747432, DOI 10.1137/0515056
- Christopher E. Heil and David F. Walnut, Continuous and discrete wavelet transforms, SIAM Rev. 31 (1989), no. 4, 628–666. MR 1025485, DOI 10.1137/1031129
- Qing Tang Jiang and Li Zhong Peng, Casimir operator and wavelet transform, Harmonic analysis in China, Math. Appl., vol. 327, Kluwer Acad. Publ., Dordrecht, 1995, pp. 125–134. MR 1355799
- G. Kaiser, “A Friendly Guide to Wavelet”, Birkhäuser, 1994.
- E. G. Kalnins and W. Miller Jr., A note on group contractions and radar ambiguity functions, Radar and sonar, Part II, IMA Vol. Math. Appl., vol. 39, Springer, New York, 1992, pp. 71–82. MR 1223151, DOI 10.1007/978-1-4684-7832-7_{7}
- F. Alberto Grünbaum, Marvin Bernfeld, and Richard E. Blahut (eds.), Radar and sonar. Part II, The IMA Volumes in Mathematics and its Applications, vol. 39, Springer-Verlag, New York, 1992. MR 1223148, DOI 10.1007/978-1-4684-7832-7
- Wilhelm Magnus, Fritz Oberhettinger, and Raj Pal Soni, Formulas and theorems for the special functions of mathematical physics, Third enlarged edition, Die Grundlehren der mathematischen Wissenschaften, Band 52, Springer-Verlag New York, Inc., New York, 1966. MR 0232968, DOI 10.1007/978-3-662-11761-3
- F. Alberto Grünbaum, Marvin Bernfeld, and Richard E. Blahut (eds.), Radar and sonar. Part II, The IMA Volumes in Mathematics and its Applications, vol. 39, Springer-Verlag, New York, 1992. MR 1223148, DOI 10.1007/978-1-4684-7832-7
- P. Morse, Diatomic molecules according to the wave mechanics. II. Vibrational levels, Physical Review, 34(1929), 57-64.
- Harold Naparst, Dense target signal processing, IEEE Trans. Inform. Theory 37 (1991), no. 2, 317–327. MR 1093746, DOI 10.1109/18.75247
- W. Schempp, Harmonic analysis on the Heisenberg nilpotent Lie group, with applications to signal theory, Pitman Research Notes in Mathematics Series, vol. 147, Longman Scientific & Technical, Harlow; John Wiley & Sons, Inc., New York, 1986. MR 872095
- D. Swick, An ambiguity function independent of assumption about bandwidth and carrier frequency, NRL Report 6471, Washington, DC, 1966.
- D. Swick, A review of wide-band ambiguity function, NRL Report 6994, Washington, DC, 1969.
- L. Weiss, Wavelets and wideband correlation processing, IEEE Signal Proc. Magazine, Jan. 1994, 13-32.
- F. Alberto Grünbaum, Marvin Bernfeld, and Richard E. Blahut (eds.), Radar and sonar. Part II, The IMA Volumes in Mathematics and its Applications, vol. 39, Springer-Verlag, New York, 1992. MR 1223148, DOI 10.1007/978-1-4684-7832-7
- P. M. Woodward, Probability and information theory, with applications to radar, 2nd ed., Pergamon Press, Oxford-Edinburgh-New York-Paris-Frankfurt, 1964. MR 0180402
- Randy K. Young, Wavelet theory and its applications, The Kluwer International Series in Engineering and Computer Science, vol. 189, Kluwer Academic Publishers, Boston, MA, 1993. With a foreword by N. K. Bose. MR 1256490, DOI 10.1007/978-1-4615-3584-3
Bibliographic Information
- Qingtang Jiang
- Affiliation: Department of Mathematics, Peking University, Beijing 100871, People’s Republic of China
- Address at time of publication: Department of Mathematics, National University of Singapore, Lower Kent Ridge Road, Singapore 119260
- Email: qjiang@haar.math.nus.sg
- Received by editor(s): October 25, 1995
- Received by editor(s) in revised form: August 23, 1996
- Communicated by: J. Marshall Ash
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 561-567
- MSC (1991): Primary 42C05, 42C99
- DOI: https://doi.org/10.1090/S0002-9939-98-04197-5
- MathSciNet review: 1443157