Wavelet analysis of bender element signals

Accurate determination of shear wave arrival time using bender elements may be severely affected by a combination of near-field effects and reflected waves. These may mask the first arrival of the shear wave, making its detection difficult in the time domain. This paper describes an approach for measuring the shear wave arrival time through analysis of the output signal in the time-scale domain using a multi-scale wavelet transform. The local maxima lines of the wavelet transform modulus are observed at different scales, and all singularities are mathematically characterised, allowing subsequent detection of the singularity relating to the first arrival. Examples of the use of this approach on typical synthetic and experimental bender element signals are also supplied, and these results are compared with those from other time and frequency domain approaches. The wavelet approach is not affected by near-field effects, but instead is characterised by a relatively consistent singularity related to the shear wave arrival time, across a range of frequencies and noise levels.

Wavelet phase coherence analysis: Application to a quiet-sun magnetic element

A new application of wavelet analysis is presented that utilizes the inherent phase information residing within the complex Morlet transform. The technique is applied to a weak solar magnetic network region, and the temporal variation of phase difference between TRACE 1700 Angstrom and SOHO/SUMER C II 1037 Angstrom intensities is shown. We present, for the first time in an astrophysical setting, the application of wavelet phase coherence, including a comparison between two methods of testing real wavelet phase coherence against that of noise. The example highlights the advantage of wavelet analysis over more classical techniques, such as Fourier analysis, and the effectiveness of the former to identify wave packets of similar frequencies but with differing phase relations is emphasized. Using cotemporal, ground-based Advanced Stokes Polarimeter measurements, changes in the observed phase differences are shown to result from alterations in the magnetic topology.

Comparison of Wavelet Transform and Time-Domain Analysis of Second Trimester Uterine Artery Doppler Waveforms in Screening for Pre-Eclampsia

The aim of this study was to compare time-domain waveform analysis of second-trimester uterine artery Doppler using the resistance index (RI) with waveform analysis using a mathematical tool known as wavelet transform for the prediction of pre-eclampsia (PE). This was a retrospective, nested case-cohort study of 336 women, 37 of whom subsequently developed PE. Uterine artery Doppler waveforms were analysed using both RI and waveform analysis. The utility of these indices in screening for PE was then evaluated using receiver operating characteristic curves. There were significant differences in uterine artery RI between the PE women and those with normal pregnancy outcome. After wavelet analysis, significant difference in the mean amplitude in wavelet frequency band 4 was noted between the 2 groups. The sensitivity for both Doppler RI and frequency band 4 for the detection of PE at a 10% false-positive rate was 45%. This small study demonstrates the application of wavelet transform analysis of uterine artery Doppler waveforms in screening for PE. Further prospective studies are needed in order to clearly define if this analytical approach to waveform analysis may have the potential to improve the detection of PE by uterine artery Doppler screening.

Wavelets for the Analysis and Compression of Power System Disturbances

Wavelets introduce new classes of basis functions for time-frequency signal analysis and have properties particularly suited to the transient components and discontinuities evident in power system disturbances. Wavelet analysis involves representing signals in terms of simpler, fixed building blocks at different scales and positions. This paper examines the analysis and subsequent compression properties of the discrete wavelet and wavelet packet transforms and evaluates both transforms using an actual power system disturbance from a digital fault recorder. The paper presents comparative compression results using the wavelet and discrete cosine transforms and examines the application of wavelet compression in power monitoring to mitigate against data communications overheads.

The application of a Trous wave filtering and Monte Carlo analysis on secis 2001 solar eclipse observations

Eight thousand images of the solar corona were captured during the June 2001 total solar eclipse. New software for the alignment of the images and an automated technique for detecting intensity oscillations using multi-scale wavelet analysis were developed. Large areas of the images covered by the Moon and the upper corona were scanned for oscillations and the statistical properties of the atmospheric effects were determined. The a Trous wavelet transform was used for noise reduction and Monte Carlo analysis as a significance test of the detections. The effectiveness of those techniques is discussed in detail.

Rapid design of discrete orthonormal wavelet transforms using silicon IP components

A rapid design methodology for orthonormal wavelet transform cores has been developed. This methodology is based on a generic, scaleable architecture utilising time-interleaved coefficients for the wavelet transform filters. The architecture has been captured in VHDL and parameterised in terms of wavelet family, wavelet type, data word length and coefficient word length. The control circuit is embedded within the cores and allows them to be cascaded without any interface glue logic for any desired level of decomposition. Case studies for stand alone and cascaded silicon cores for single and multi-stage wavelet analysis respectively are reported. The design time to produce silicon layout of a wavelet based system has been reduced to typically less than a day. The cores are comparable in area and performance to handcrafted designs. The designs are portable across a range of foundries and are also applicable to FPGA and PLD implementations.

An indirect bridge inspection method incorporating a wavelet-based damage indicator and pattern recognition

In recent years, there has been a move towards the development of indirect structural health monitoring (SHM)techniques for bridges; the low-cost vibration-based method presented in this paper is such an approach. It consists of the use of a moving vehicle fitted with accelerometers on its axles and incorporates wavelet analysis and statistical pattern recognition. The aim of the approach is to both detect and locate damage in bridges while reducing the need for direct instrumentation of the bridge. In theoretical simulations, a simplified vehicle-bridge interaction model is used to investigate the effectiveness of the approach in detecting damage in a bridge from vehicle accelerations. For this purpose, the accelerations are processed using a continuous wavelet transform as when the axle passes over a damaged section, any discontinuity in the signal would affect the wavelet coefficients. Based on these coefficients, a damage indicator is formulated which can distinguish between different damage levels. However, it is found to be difficult to quantify damage of varying levels when the vehicle’s transverse position is varied between bridge crossings. In a real bridge field experiment, damage was applied artificially to a steel truss bridge to test the effectiveness of the indirect approach in practice; for this purpose a two-axle van was driven across the bridge at constant speed. Both bridge and vehicle acceleration measurements were recorded. The dynamic properties of the test vehicle were identified initially via free vibration tests. It was found that the resulting damage indicators for the bridge and vehicle showed similar patterns, however, it was difficult to distinguish between different artificial damage scenarios.

Wavelet entropy of Doppler ultrasound blood velocity flow waveforms distinguishes nitric oxide-modulated states

Wavelet entropy assesses the degree of order or disorder in signals and presents this complex information in a simple metric. Relative wavelet entropy assesses the similarity between the spectral distributions of two signals, again in a simple metric. Wavelet entropy is therefore potentially a very attractive tool for waveform analysis. The ability of this method to track the effects of pharmacologic modulation of vascular function on Doppler blood velocity waveforms was assessed. Waveforms were captured from ophthalmic arteries of 10 healthy subjects at baseline, after the administration of glyceryl trinitrate (GTN) and after two doses of N(G)-nitro-L-arginine-methyl ester (L-NAME) to produce vasodilation and vasoconstriction, respectively. Wavelet entropy had a tendency to decrease from baseline in response to GTN, but significantly increased after the administration of L-NAME (mean: 1.60 ± 0.07 after 0.25 mg/kg and 1.72 ± 0.13 after 0.5 mg/kg vs. 1.50 ± 0.10 at baseline, p < 0.05). Relative wavelet entropy had a spectral distribution from increasing doses of L-NAME comparable to baseline, 0.07 ± 0.04 and 0.08 ± 0.03, respectively, whereas GTN had the most dissimilar spectral distribution compared with baseline (0.17 ± 0.08, p = 0.002). Wavelet entropy can detect subtle changes in Doppler blood velocity waveform structure in response to nitric-oxide-mediated changes in arteriolar smooth muscle tone.

Observational Evidence for Mode Coupling in the Chromospheric Network

Oscillations in network bright points (NBPs) are studied at a variety of chromospheric heights. In particular, the three-dimensional variation of NBP oscillations is studied using image segmentation and cross-correlation analysis between images taken in light of Ca II K3, Ha core, Mg I b2, and Mg I b1-0.4 Å. Wavelet analysis is used to isolate wave packets in time and to search for height-dependent time delays that result from upward- or downward-directed traveling waves. In each NBP studied, we find evidence for kink-mode waves (1.3, 1.9 mHz), traveling up through the chromosphere and coupling with sausage-mode waves (2.6, 3.8 mHz). This provides a means for depositing energy in the upper chromosphere. We also find evidence for other upward- and downward-propagating waves in the 1.3-4.6 mHz range. Some oscillations do not correspond to traveling waves, and we attribute these to waves generated in neighboring regions.

White-light oscillations during a flare on II Peg

We analyse the intensity oscillations observed in the gradual phase of a white-light flare on the RS CV n binary II Peg. Fast Fourier Transform power spectra and Wavelet analysis reveal a period of 220 s. The reliability of the oscillation is tested using several criteria. Oscillating coronal loop models are used to derive physical parameters such as temperature, electron density and magnetic field strength associated with the coronal loop. The derived parameters are consistent with the near-simultaneous X-ray observations of the flare. There is no evidence for oscillations in the quiescent state of the binary.

Propagating waves and magnetohydrodynamic mode coupling in the quiet-sun network

High-cadence multiwavelength optical observations were taken with the Dunn Solar Telescope at the National Solar Observatory, Sacramento Peak, accompanied by Advanced Stokes Polarimeter vector magnetograms. A total of 11 network bright points (NBPs) have been studied at different atmospheric heights using images taken in wave bands centered on Mg I b(1) - 0.4 Angstrom, Halpha, and Ca II K-3. Wavelet analysis was used to study wave packets and identify traveling magnetohydrodynamic waves. Wave speeds were estimated through the temporal cross-correlation of signals, in selected frequency bands of wavelet power, in each wavelength. Four mode-coupling cases were identified, one in each of four of the NBPs, and the variation of the associated Fourier power with height was studied. Three of the detected mode-coupling, transverse-mode frequencies were observed in the 1.2-1.6 mHz range (mean NBP apparent flux density magnitudes over 99-111 Mx cm(-2)), with the final case showing 2.0-2.2 mHz (with 142 Mx cm(-2)). Following this, longitudinal-mode frequencies were detected in the range 2.6-3.2 mHz for three of our cases, with 3.9-4.1 mHz for the remaining case. After mode coupling, two cases displayed a decrease in longitudinal-mode Fourier power in the higher chromosphere.

Eclipse observations of high-frequency oscillations in active region coronal loops

One of the mechanisms proposed for heating the corona above solar active regions is the damping of magnetohydrodynamic (MHD) waves. Continuing on previous work, we provide observational evidence for the existence of high-frequency MHD waves in coronal loops observed during the August 1999 total solar eclipse. A wavelet analysis is used to identify twenty 4 x 4 arcsec(2) areas showing intensity oscillations. All detections lie in the frequency range 0.15 - 0.25 Hz (7 - 4 s), last for at least 3 periods at a confidence level of more than 99% and arise just outside known coronal loops. This leads us to suggest that they occur in low emission-measure or different temperature loops associated with the active region.

Twisting flux tubes as a cause of micro-flaring activity

High-cadence optical observations of an H-alpha blue-wing bright point near solar AR NOAA 10794 are presented. The data were obtained with the Dunn Solar Telescope at the National Solar Observatory/Sacramento Peak using a newly developed camera system, the RAPID DUAL IMAGER. Wavelet analysis is undertaken to search for intensity-related oscillatory signatures, and periodicities ranging from 15 to 370 s are found with significance levels exceeding 95%. During two separate microflaring events, oscillation sites surrounding the bright point are observed to twist. We relate the twisting of the oscillation sites to the twisting of physical flux tubes, thus giving rise to reconnection phenomena. We derive an average twist velocity of 8.1 km s(-1) and detect a peak in the emitted flux between twist angles of 180 degrees and 230 degrees.

High-frequency oscillations in a solar active region observed with the RAPID DUAL IMAGER

High-cadence, synchronized, multiwavelength optical observations of a solar active region (NOAA 10794) are presented. The data were obtained with the Dunn Solar Telescope at the National Solar Observatory/Sacramento Peak using a newly developed camera system: the rapid dual imager. Wavelet analysis is undertaken to search for intensity related oscillatory signatures, and periodicities ranging from 20 to 370 s are found with significance levels exceeding 95%. Observations in the H-α blue wing show more penumbral oscillatory phenomena when compared to simultaneous G-band observations. The H-α oscillations are interpreted as the signatures of plasma motions with a mean velocity of 20 km s-1. The strong oscillatory power over H-α blue-wing and G-band penumbral bright grains is an indication of the Evershed flow with frequencies higher than previously reported.