Asymptotic wavelet and Gabor analysis: extraction of instantaneous frequencies
- 1 March 1992
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 38 (2), 644-664
- https://doi.org/10.1109/18.119728
Abstract
The behavior of the continuous wavelet and Gabor coefficients in the asymptotic limit using stationary phase approximations are investigated. In particular, it is shown how, under some additional assumptions, these coefficients allow the extraction of some characteristics of the analyzed signal, such as frequency and amplitude modulation laws. Applications to spectral line estimations and matched filtering are briefly discussed.<>Keywords
This publication has 11 references indexed in Scilit:
- Wavelets associated with representations of the affine Weyl–Heisenberg groupJournal of Mathematical Physics, 1991
- The wavelet transform, time-frequency localization and signal analysisIEEE Transactions on Information Theory, 1990
- Clutter interference and the integration time of echoes in the echolocating bat, E p t e s i c u s f u s c u sThe Journal of the Acoustical Society of America, 1989
- Orthonormal bases of compactly supported waveletsCommunications on Pure and Applied Mathematics, 1988
- Time-frequency localisation operators-a geometric phase space approach: II. The use of dilationsInverse Problems, 1988
- Transforms associated to square integrable group representations. I. General resultsJournal of Mathematical Physics, 1985
- Decomposition of Hardy Functions into Square Integrable Wavelets of Constant ShapeSIAM Journal on Mathematical Analysis, 1984
- Analysis of time-varying signals with small BT valuesIEEE Transactions on Acoustics, Speech, and Signal Processing, 1978
- Asymptotic ExpansionsPublished by Cambridge University Press (CUP) ,1965
- A product theorem for Hilbert transformsProceedings of the IEEE, 1963