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| Latest News |
Why Use the S-Transform
the S-transform approach has the following unique
properties:
1. a direct connection to the Fourier transform through the inverse ST, and a
direct connection to the time series through the direct signal extraction.
2. frequency invariant amplitude response.
3. absolutely referenced phase properties.
4. progressive resolution.
The ST uniquely combines the qualities these characteristics. It simultaneously
estimates the local amplitude spectrum and the local phase spectrum, whereas a
wavelet approach is only capable of probing the local amplitude/power spectrum.
The ST fully represents the amplitude of all signals, in contrast to the CWT which
attenuates high frequencies. It independently probes the positive frequency spectrum
and the negative frequency spectrum, whereas many wavelet approaches are
incapable of being applied to a complex time series. It is sampled at the discrete
Fourier transform frequencies unlike the CWT where the sampling is arbitrary. Because
of the absolutely referenced phase of the S-transform, it is possible to define a
channel Instantaneous Frequency function for each voice [22]. It is possible to perform
a localized cross spectral analysis as shown in [23, 24] where transient wavelike
motions were detected in the time series measured by spaced receivers (physically
separated by a known distance). By analyzing phase shifts in the S-transforms of
the two time series, the phase speed of the wavelike motion was deduced. Such a
straightforward analysis is not possible with a wavelet type approach.
The manuscript titled "Why Use the S-Transform?" is available here:
 Download
R. G. Stockwell
Why use the S-Transform
Fields Institute Communications
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New S-Transform Paper
A paper titled Denoising of seismograms using the S transform has been published.
Parolai (2009) Denoising of seismograms using the S transform
BSSA, 99,226-234.
by Dr. Stefano Parolai of the Helmholtz Centre, Potsdam,
German Research Centre for Geosciences
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Google Earth Visualizations
There are new animations of the global data sets of ocean surface vector winds now available.
Click here to go to the Google Earth Page.
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Note on forum
This forum has been flooded by bots lately, and it results in hundreds of email failure messages per day. Temporarily, the sign-up feature has been disabled (and in the future an entire new software suite will be employed for this webpage). If you wish to sign up, just send an email to me, or to webmaster@cora.nwra.com. Sorry for the inconvenience.
Or, one can use the Comment section below. I will monitor that regularly.
-bob
Digital Imaging publication
Sylvia Drabycz et al. published a paper employing the orthonormal ST in the Journal of Digital Imaging. It is available online (link below)
Abstract:
We present a new efficient approach for characterizing image texture based on a recently published discrete, orthonormal space-frequency transform known as the DOST. We develop a frequency-domain implementation of the DOST in two dimensions for the case of dyadic frequency sampling. Then, we describe a rapid and efficient approach to obtain local spatial frequency information for an image and show that this information can be used to characterize the horizontal and vertical frequency patterns in synthetic images. Finally, we demonstrate that DOST components can be combined to obtain a rotationally invariant set of texture features that can accurately classify a series of texture patterns. The DOST provides the computational efficiency and multi-scale information of wavelet transforms, while providing texture features in terms of Fourier frequencies. It outperforms leading wavelet-based texture analysis methods.
http://www.springerlink.com/content/t5j2p45h00482727/
Recent Publications- November 2007
Recently 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-Transform
This paper is available for download:
Download
The 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.
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Recent Publications - November 2006
A 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 Flowmetry
Here 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
LINK
Recent Publications
A paper employing two dimensional S-Transform analysis
of 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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2D computational complexity and visualization
Posted on: 2009-04-17 16:07:07
By: Anonymous
|
Edited By: stockwell
On: 2009-05-11 11:27:21
|
Hi Bob-
I'm considering the use of the ST to quantify the space-time structure of a series of weather radar reflectivity images (i.e., interested to see how small/large scales of precipitation patterns observed by weather radar behave over time)...
1) What is your opinion on using the ST for such a task? And do you know of anyone who has applied the ST in such a way?
2) What is your recommendation for reducing the computational complexity of the ST for such a task? I will be considering about 10 images (matrices) of dimension 281 X 281.
3) What is your recommendation for visualizing the results in the most tractable way? Ideally this would be a 3D plot with 2 Cartesian coordinate axes with the third axes representing intensity by intensity (darkness) level.
Many thanks,
Evan
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