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Recent Publications- November 2007Recently PUBLISHED: 1) Stockwell, R. G., D. M. Riggin, W. J. R. French, G. B. Burns, and D. J. Murphy (2007), Planetary waves and intraseasonal oscillations at Davis, Antarctica, from undersampled time series, J. Geophys. Res., 112, D21107, doi:10.1029/2006JD008034, 13 November 2007 2) (chapter in a book) "Why use the ST?" by Robert Stockwell, Pseudo-Differential Operators: Partial Differential Equations and Time-Frequency Analysis Edited by: Luigi Rodino, Università di Torino, Italy, Bert-Wolfgang Schulze, Universität Potsdam, Germany, and M. W. Wong, York University, Toronto, ON, Canada (link: http://www.ams.org/bookstore?fn=20&arg1=ficseries&item=FIC-52) Orthogonal Basis for the S-TransformThis paper is available for download:  DownloadThe citation is: "A basis for efficient representation of the S-transform" R.G. Stockwell, Digital Signal Processing Volume 17, Issue 1, January 2007, Pages 371-393 A recent paper describes an orthogonal basis for the S-Transform. Currently, the ST of a N-point time series returns a matrix with N^2 points. This can get quite large as N increases, and limits the utility of the ST. The new orthogonal representation allows one to take an N-point time series and return an N_point local spectrum representation. Thus allowing the application of the ST to almost arbitrarily large data sets. Stockwell, R.G. A Basis for Efficient Representation of the S-Transform, Digital Signal Processing, doi:10.1016/j.dsp.2006.04.006 (Article in Press) (2006a) It is available online at: http://doi.org/ past in the doi number above: doi:10.1016/j.dsp.2006.04.006 ABSTRACT: The S-transform is a time-frequency representation known for its local spectral phase properties. A key feature of the S-transform is that it uniquely combines a frequency dependent resolution of the time-frequency space and absolutely referenced local phase information. This allows one to define the meaning of phase in a local spectrum setting, and results in many desirable characteristics. One drawback to the S-transform is the redundant representation of the time-frequency space and the consumption of computing resources this requires (a characteristic it shares with the continuous wavelet transform, the short time Fourier transform, and Cohen's class of generalized time-frequency distributions). The cost of this redundancy is amplified in multidimensional applications such as image analysis. A more efficient representation is introduced here as a orthogonal set of basis functions that localizes the spectrum and retains the advantageous phase properties of the S-transform. These basis functions are defined to have phase characteristics that are directly related to the phase of the Fourier transform spectrum, and are both compact in frequency and localized in time. Distinct from a wavelet approach, this approach allows one to directly collapse the orthogonal local spectral representation over time to the complex-valued Fourier transform spectrum. Because it maintains the phase properties of the S-transform, one can perform localized cross spectral analysis to measure phase shifts between each of multiple components of two time series as a function of both time and frequency. In addition, one can define a generalized instantaneous frequency (IF) applicable to broadband nonstationary signals. This is the first time a channel IF has been integrated in an orthogonal local spectral representation. A direct comparison between these basis functions and complex wavelets is performed, highlighting the advantages of this approach. The relationship between this basis set and the fully redundant S-transform is demonstrated highlighting the ability to arbitrarily sample the time-frequency space. The introduction of this basis set leads to efficient analysis routines that may find use in a wide range of fields. Recent Publications - November 2006A couple of recent papers have been published:Fritts, D.C., D. Janches, D.M. Riggin, R.G. Stockwell, M.P. Sulzer, and S. Gonzalez, Gravity waves and momentum fluxes in the mesosphere and lower thermosphere using 430 MHz dual-beam measurements at Arecibo: 2. Frequency spectra, momentum fluxes, and variability. J. Geophys. Res., 111, D18108, doi:10.1029/2005JD006883, 2006. Abstract: Janches et al. (2006) described a new dual-beam use of the 430 MHz incoherent scatter radar at the Arecibo Observatory in Puerto Rico. We found the technique to define the radial wind field in the mesosphere and lower thermosphere with sufficient accuracy to characterize gravity waves occurring at high frequencies and small spatial scales over an extended altitude range. The coplanar, dual-beam experiment was also designed to test the ability of the system to measure gravity wave momentum fluxes and their frequency distributions, and we report here on those results. Initial measurements were of limited duration and necessarily represent a case study, but they demonstrate the value of such measurements for studies of GW variability and large-scale interactions. Radial velocity variances reveal preferential eastward propagation for most intervals and altitudes, with the greatest propagation bias at lower altitudes and later times on 11 September when strong westward mean winds favor strong gravity filtering. The momentum fluxes observed during this experiment had ∼50-min averages that were often near zero, occasionally achieved amplitudes of ∼20 to 50 m2s−2, displayed significant consistency in altitude, and exhibited an approximate anticorrelation with the zonal wind field in cases with significant momentum fluxes. Frequency spectra defined the major contributions to the momentum fluxes, while S transforms were employed to examine the temporal variability of the GWs and momentum fluxes in greater detail. Laser Doppler FlowmetryHere is the reference of Said Assous' paper published this month."S-Transform Applied to Laser Doppler Flowmetry Reactive Hyperemia Signals" Assous, S.; Humeau, A.; Tartas, M.; Abraham, P.; L'Huillier, J.P. IEEE Trans Biomed Eng. 2006 Jun;53(6):1032-7 Digital Object Identifier 10.1109/TBME.2005.863843 LINKRecent PublicationsA paper employing two dimensional S-Transform analysisof gravity (buoyancy) waves seen in atmospheric airglow layers has been published. The reference is: Stockwell, R. G., M. J. Taylor, K. Nielsen, and M. J. Jarvis (2006), A novel joint space-wavenumber analysis of an unusual Antarctic gravity wave event, Geophys. Res. Lett., 33, L08805, doi:10.1029/2005GL025660. a related paper is: Nielsen, K.; Taylor, M. J.; Stockwell, R. G.; Jarvis, M. J. An unusual mesospheric bore event observed at high latitudes over Antarctica, Geophys. Res. Lett., Vol. 33, No. 7, L0780310.1029/2005GL025649 05 April 2006
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