Letter to the editor: Stockwell and wavelet transforms

Journal of Fourier Analysis and Applications

Volumn 12, Issue 6, 2006, Pages 713-721

  Gibson, Peter C ^a   Lamoureux, Michael P ^b   Margrave, Gary F ^b  

^a YORK UNIVERSITY   (Canada)

^b UNIVERSITY OF CALGARY   (Canada)

Author keywords

Continuous wavelet transform; Resolution of identity; Stockwell transform

Indexed keywords

EID: 33847001214     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00041-006-6087-9     Document Type: Article

References (55)

1. Andino, S., Menendez, R., Lantz, C., Blank, O., Michel, G, and Landis, T. (2001). Nonstationary distributed source approximation: An alternative to improve localization procedures, Human Brain Mapping 14.
2. Assous, S., Humeau, A., Tartas, M., Abraham, P., and L'Huillier, J. (2006). S-transform applied to laser doppler flowmetry reactive hyperemia signals, IEEE Trans. Biomed. Eng. 53, 1032-1037.
3. Bros, J. and Iagolnitzer, D. (1975). Support essential et structure analytique des distributions, Seminaire Goulaouic-Lions-Schwartz, exp. no. 18.
4. Chu, P. ( 1994). A high resolution global sea surface temperature analysis and climatology, Tropical Oceans Global Atmosphere Notes 17, 5-7.
5. Cook, J. and McFadden, P. (1996). Decomposition of gear vibration signals by the generalized S-transform, (I) Gaussian windows, Report OUEL.
6. Cordoba, A. and Fefferman, C. (1978). Wave packets and Fourier integral operators, Comm. Partial Differential Equations 3, 979-1005.
7. Czaja, W., Kutyniok, G., and Speegle, D. (2006). The geometry of sets of parameters of wave packet frames, Appl. Comput. Harmon. Anal. 20, 108-125.
8. Dahlke, S., Fornasier, M., Rauhaut, R., Steidl, G., and Tesche, G. (2005). Generalized coorbit theory, Banach frames, and the relation to alpha-modulation spaces, Philipps-Universitt Marburg, Bericht No. 2005-6.
9. Dash, P., Panigrahi, B., and Panda, G. (2003). Power quality analysis using S-transform, IEEE Trans. On Power Deliveiy 18.
10. Dash, P., Panigrahi, B., Sahoo, D., and Panda, G. (2003). Power quality disturbance data compression, detection, and classification using integrated spline wavelet and S-transform, IEEE Trans. On Power Delivery 18.
11. Daubechies, I. (1992). Ten Lectures on Wavelets, CBMS-NSF Regional conference series in applied mathematics, Academic Press.
12. Du, J., Wong, M., and Zhu, H. (2006). Continuous and discrete inversion formulas for the Stockwell transform, Integral Transforms Spec. Funct., to appear.
13. Eramian, M., Schincariol, R., Mansinha, L., and Stockwell, R. (1999). Generation of aquifer heterogeneity maps using two-dimensional spectral texture segmentation techniques, Mathematical. Geology 31.
14. Eramian, M., Schincariol, R., Stockwell, R., Lowe, R., and Mansinha, L. (1996). Review of applications of ID and 2D S-transforms, Wavelet Applications IV 3078.
15. Espy, P., Hibbins, R., Jones, G., Riggin, D., and Fritts, D. (2003). Rapid, large-scale temperature changes in the polar mesosphere and their relationship to meridional flows, Geophysical Research Letters 30.
16. Fornasier, M. (2006). Banach frames for α-modulation spaces, Appl. Comput. Harm. Anal., to appear.
17. Fritts, D., Riggin, D., Balsley, B., and Stockwell, R. (1998). Recent results with an MF radar at McMurdo, Antarctica: Characteristics and variability of motions near 12-hour period in the mesosphere, Geophysical Research Letters 25, 297-300.
18. Gao, J., Chen, W., Li, Y, and Tian, F. (2003). Generalized S-transform and seismic response analysis of thin interbeds, Chinese J. Geophysics 46, Chinese Ed.
19. Grinsted, A. (2004). Matlab wavelet coherence package, http://www.pol.ac.uk/home/research/waveletcoherence/, includes code by C. Torrence and G. P. Campo.
20. Holschneider, M. and Nazaret, B. (2003). An interpolation family between Gabor and wavelet transformations, in Advances in Partial Differential Equations, Alberverios, Demuth, Schrohe, Schulze, Eds., Wiley, 363-394.
21. Lee, I. and Dash, P. (2003). S-transform-based intelligent system for classification of power quality disturbance signals, IEEE Trans. On Industrial Electronics 50.
22. Linfoot, B. and Wolfram, J. (2000). Modulational interactions of broad-band gravity waves observed during N-sea storms, IFREMER Rogue waves workshop, November.
23. Liu, H. and Roble, R. (2002). A study of a self-generated stratospheric sudden warming and its mesospheric-lower thermospheric impacts using the coupled TIME-GCM/CCM3, J. Geophysical Research-Atmospheres 107.
24. Mallat, S. (1999). A Wavelet Tour of Signal Processing, Academic Press.
25. Mansinha, L., Stockwell, R., and Lowe, R. (1997). Pattern analysis with two-dimensional spectral localisation: Applications of two-dimensional S-transforms, PhysicaA 239, 286-295.
26. Mansinha, L., Stockwell, R., Lowe, R., Eramian, M., and Schincariol, R. (1997). Local S-spectrum analysis of 1-D and 2-D data. Physics of the Earth and Planetary Interiors 103.
27. McFadden, P. (2000). Detection of gear faults by decomposition of matched differences of vibration signals, Mechanical Systems Signal Processing 14.
28. Merzlyakov, E., Portnyagin, Y, Jacobi, C., Mitchell, N., Muller, H., Manson, A., Fachrutdinova, A., Singer, W., and Hoffmann, P. (2001). On the longitudinal structure of the transient day-to-day variation of the semidiurnal tide in the mid-latitude lower thermosphere-I, winter season, Ann. Geophysicae 19.
29. Merzlyakov, E., Portnyagin, Y., Makarov, N., Forbes, J., and Palo, S. (1999). Intradiurnal wind variations in the lower thermosphere over the Antarctic from meteor radar measurements, Izvestiya Akademii Nauk Fizika Atmosfery I Okeana 35.
30. Merzlyakov, E., Portnyagin, Y., Makarov, N., Forbes, J., and Palo, S. (2001). Interdiurnal wind oscillations in the Antarctic lower thermosphere from meteor radar measurements at the Amundsen-Scott and Molodezhnaya stations, Izvestiya Atmospheric and Oceanic Physics 37.
31. Merzlyakov, E., Portnyagin, Y, Makarov, N., Forbes, J., and Palo, S. (2003). Some results of simultaneous meteor radar measurements of wind at the Obninsk and Dixon stations, Izvestiya Atmospheric and Oceanic Physics 39.
32. Mitchell, J.R., Fong, T.C., Zhu, H., Goodyear, B.C., and Brown, R. (2005). Local multi-scale Fourier analysis for MRI, U. S. patent 6,850,062.
33. Morlet, J., Arens, G., Fourgeau, E., and Giard, D. (1982). Wave propagation and sampling theory-Part I: Complex signal and scattering in multilayered media, Geophysics 47, 203-221.
34. Oldenborger, G., Schincariol, R., and Mansinha, L. (2002). Space-local spectral texture segmentation applied to characterizing the heterogeneity of hydraulic conductivity, Water Resources Research 38.
35. Osler, J. and Chapman, D. (1996). Seismo-acoustic determination of the shear-wave speed of surficial clay and silt sediments on the Scotian shelf, Canadian Acoustics 24, 11-22.
36. Pancheva, D., Merzlyakov, E., Mitchell, N., Portnyagin, Y, Manson, A., Jacobi, C., Meek, C., Luo, Y., Clark, R., Hocking, W., MacDougall, J., Muller, H., Kurschner, D., Jones, G., Vincent, R., Reid, L, Singer, W., Igarashi, K., Fraser, G., Fahrutdinova, A., Stepanov, A., Poole, L., Malinga, S., Kashcheyev, B., and Oleynikov, A. (2002). Global-scale tidal variability during the PSMOS campaign of June-August 1999: Interaction with planetary waves, J. Atmospheric Solar-Terrestrial Physics 64.
37. Pinnegar, C. and Mansinha, L. (2003). The bi-Gaussian S-transform, SIAM J. Sci. Comput. 24.
38. Pinnegar, C. and Mansinha, L. (2003). The S-transform with windows of arbitrary and varying shape, Geophysics 68, 381-385.
39. Portnyagin, Y., Forbes, J., Merzlyakov, E., Makarov, M., and Palo, S. (2000). Intradiurnal wind variations observed in the lower thermosphere over the south pole, Annales Geophysicae-Atmospheres Hydrospheres and Space Sciences 18, 547-554.
40. Portnyagin, Y., Merzlyakov, E., Jacobi, C., Mitchell, N., Muller, H., Manson, A., Singer, W., Hoffman, P., and Fachratdinova, A. (2005). Some approaches to the global scale analysis of the lower thermosphere wind data, preprint.
41. Portnyagin, Y., Merzlyakov, E., Jacobi, C., Mitchell, N., Muller, H., Manson, A., Singer, W., Hoffmann, P., and Fachrutdinova, A. (1999). Some results of S-transform analysis of the transient planetary-scale wind oscillations in the lower thermosphere, Earth Planets and Space 51, 711-717.
42. Qian, S. (2002). Time-Frequency and Wavelet Transforms, Prentice-Hall.
43. Rao, R. M. and Bopardikar, A. S. (1998). Wavelet Transforms, Addison-Welsey.
44. Riggin, D., Fritts, D., Jarvis, M., and Jones, G. (1999). Spatial structure of the 12-hour wave in the Antarctic as observed by radar, Earth Planets and Space 51.
45. Stockwell, R. and Lowe, R. (2001). Airglow imaging of gravity waves 1. Results from a small network of OH nightglow scanning imagers, J. Geophysical Research-Atmospheres 106.
46. Stockwell, R., Mansinha, L., and Lowe, R. (1996). Localization of the complex spectrum: The S-transform, IEEE Tmns. Signal Process. 44, 998-1001.
47. Stockwell, R., Mansinha, L., and Löwe, R. (1996). Localization of the complex spectrum: The S-transform (proceedings), J. Association Exploration Geophysicists 17, 99-114.
48. Stockwell, R. G. (1996). Matlabst.m code, http://www.cora.nwra.com/ ~stockwel/, from article "Localization of the complex spectrum: The S-transform."
49. Talaat, E., Yee, J., and Zhu, X. (2002). The 6.5-day wave in the tropical stratosphere and mesosphere, J. Geophysical Research-Atmospheres 107.
50. Theophanis, S. and Queen, J. (2000). Color display of the localized spectrum, Geophysics 65.
51. Varanini, M., Paolis, G., Emdin, M., Macerata, A., Pola, S., Cipriani, M., and Marchesi, C. (1997). Spectral analysis of cardiovascular time series by the S-transform, Computers in Cardiology 24, 383-386.
52. Walnut, D. (2002). An Introduction to Wavelet Analysis, Applied and Numerical Harmonic Analysis, Birkhäuser.
53. Wong, M. (2006). A brief overview on forty years of pseudo-differential operators, oral presentation at the 2006 CIME Workshop on Pseudo-differential Operators, Quantization and Signals, in Cetraro, Italy.
54. Yamashita, K., Miyahara, S., Miyoshi, Y, Kawano, K., and Ninomiya, J. (2002). Seasonal variation of nonmigrating semidiurnal tide in the polar MLT region in a general circulation model, J. Atmospheric Solar-Terrestrial Physics 64.
55. Zhu, H. (2002). Lecture on the S-transform in medical imaging, February 1, 2002, Thematic Year on Numerical and Computational Challenges in Science and Engineering.