Letter to the Editor: Stockwell and Wavelet Transforms

Springer Science and Business Media LLC - Tập 12 - Trang 713-721 - 2006
Peter C. Gibson1, Michael P. Lamoureux2, Gary F. Margrave3
1Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada
2Department of Mathematics and Statistics, University of Calgary, 2500 University Avenue N.W., Calgary, AB, T2N 1N4, Canada
3Department of Geology and Geophysics, University of Calgary, 2500 University Avenue N.W., Calgary, AB, T2N 1N4, Canada

Tóm tắt

Recent applied literature introduces the Stockwell transform (S-transform) as a new approach to time-frequency analysis. It is the purpose of this letter to encourage the interaction between the wavelet and the Stockwell communities by demonstrating that—up to minor modifications—the S-transform is a special case of the well-known continuous wavelet transform via a Morlet-type mother wavelet, with the features of a linear frequency scale, and an amplitude and modulation adjustment in phase space. The extensive research and applications obtained for the continuous wavelet transform can therefore be directly applied to the Stockwell domain.