Letter to the Editor: Stockwell and Wavelet Transforms

Gibson, Peter C.; Lamoureux, Michael P.; Margrave, Gary F.

doi:10.1007/s00041-006-6087-9

Cited by 37 publications

(17 citation statements)

References 35 publications

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“…In its analytical form, the 1-D Stockwell transform (Stockwell et al, 1996) closely resembles a continuous wavelet transform (CWT) with a complex sinusoidal mother wavelet windowed with a scalable Gaussian window (Gibson et al, 2006). For time series data, this scalable Gaussian localises wave perturbations in the time domain through spectral localisation in the frequency domain.…”

Section: The Stockwell Transformmentioning

confidence: 99%

A two-dimensional Stockwell transform for gravity wave analysis of AIRS measurements

et al. 2016

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Abstract. Gravity waves (GWs) play a crucial role in the dynamics of the earth's atmosphere. These waves couple lower, middle and upper atmospheric layers by transporting and depositing energy and momentum from their sources to great heights. The accurate parameterisation of GW momentum flux is of key importance to general circulation models but requires accurate measurement of GW properties, which has proved challenging. For more than a decade, the nadir-viewing Atmospheric Infrared Sounder (AIRS) aboard NASA's Aqua satellite has made global, two-dimensional (2-D) measurements of stratospheric radiances in which GWs can be detected. However, one problem with current one-dimensional methods for GW analysis of these data is that they can introduce significant unwanted biases. Here, we present a new analysis method that resolves this problem. Our method uses a 2-D Stockwell transform (2DST) to measure GW amplitudes, horizontal wavelengths and directions of propagation using both the along-track and cross-track dimensions simultaneously. We first test our new method and demonstrate that it can accurately measure GW properties in a specified wave field. We then show that by using a new elliptical spectral window in the 2DST, in place of the traditional Gaussian, we can dramatically improve the recovery of wave amplitude over the standard approach. We then use our improved method to measure GW properties and momentum fluxes in AIRS measurements over two regions known to be intense hotspots of GW activity: (i) the Drake Passage/Antarctic Peninsula and (ii) the isolated mountainous island of South Georgia. The significance of our new 2DST method is that it provides more accurate, unbiased and better localised measurements of key GW properties compared to most current methods. The added flexibility offered by the scaling parameter and our new spectral window presented here extend the usefulness of our 2DST method to other areas of geophysical data analysis and beyond.

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Section: The Stockwell Transformmentioning

confidence: 99%

A two-dimensional Stockwell transform for gravity wave analysis of AIRS measurements

et al. 2016

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“…It is worth remarking that the way of deriving the estimate of the FTBPF or the HWT coherence statistical error applied in the present work is also applicable in the case of the Morlet Wavelet Transform (MWT) coherence Popiński and Kosek (2000) or the Stockwell S-Transform coherence Gibson et al (2006), Stockwell (2007), Stockwell et al (1996). This follows from the fact that the frequency domain formula for the Continuous Wavelet Transform coefficients with respect to the Morlet wavelet is analogous to the formula on the right hand side of (2), namely Gasquet and Witomski (1999) Kulesh et al (2008), Popiński and Kosek (2000).…”

Section: Discussion Of Resultsmentioning

confidence: 99%

“…The validity of the above formula was confirmed by the Monte Carlo experiments carried out in the work Popiński and Kosek (2000). Taking into account the direct relation between the MWT and the Stockwell S-transform Gibson et al (2006) it is an easy task to modify the above formula for the statistical error to obtain one that is valid in the case of the S-Transform.…”

Section: Discussion Of Resultsmentioning

confidence: 99%

Insight into the Fourier Transform Band Pass Filtering Technique

Popiński¹

2008

Artificial Satellites

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In this work theoretical foundations of the Fourier Transform Band Pass Filter (FTBPF) technique are developed which show that such procedure is applicable to extraction of irregular monochromatic oscillations with time-varying amplitudes and phases from the analyzed signal data. Considerations concerning the statistical error of the FTBPF coherence between two filtered oscillations are included. Further certain method of the filter pass-band width parameter determination is proposed and relation between applying the FTBPF to realvalued signals and forming the so called complex-valued analytic oscillations based on the Hilbert transform is indicated.

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“…where ST is the Stockwell transform. The conversion of scale to frequency (a → 1/ω) and a frequency-dependent scaling of amplitudes is advantageous in many applications which gives clear interpretation of frequency for practitioners (Gibson et al 2006). The mother wavelet is the modulated Gaussian also known as a complex Morlet wavelet (Daubechies 1992) defined as…”

Section: Methodsmentioning

confidence: 99%

On the use of Stockwell transform in structural dynamic analysis

Küyük

2015

Sadhana

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Time-frequency analysis of earthquake records using Fourier transform is a fundamental, reliable and useful tool in earthquake engineering and engineering seismology. It will be however no longer functional if the frequency variation is analysed in time domain. Short time Fourier transform is utilized for the same purpose but this has also its own limitations and restrictions. In this research, Stockwell transform (S-transform), is evaluated in investigating frequency content of signal in time domain. First, the effectiveness of S-transform was tested by a non-stationary synthetic signal series with a sum of various instantaneous time varying frequency functions. Then, transform was employed to three different earthquake waveforms of Iwate-Miyagi Nairiku earthquake (M w 6.9, 2008); recorded in near, moderate and far sites. Finally, an application was demonstrated for determining dynamic response of three-story frame structure by using El Centro earthquake compiled with harmonic motion. Unlike widely used continuous wavelet transform, which provides temporal and spectral information simultaneously, S-transform is very straightforward and easy to manipulate for interpretations. All cases considered in this research showed that Stransform can be implemented for further research activities related with frequencydependent strong motion analysis by practitioners and engineers. S-transform can distinguish abrupt frequency changes in structures effectively and accurately.

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Letter to the Editor: Stockwell and Wavelet Transforms

Cited by 37 publications

References 35 publications

A two-dimensional Stockwell transform for gravity wave analysis of AIRS measurements

A two-dimensional Stockwell transform for gravity wave analysis of AIRS measurements

Insight into the Fourier Transform Band Pass Filtering Technique

On the use of Stockwell transform in structural dynamic analysis

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