Wavelet Spectrum Research Articles

Complex-Valued Wavelet Spectrum Analysis of Respiratory Conditions and Its Feasibility in the Detection of Low-Functional Respiration.

Respiratory monitoring is a significant issue to reduce patient risks and medical staff labor in postoperative care and epidemic infection, particularly after the COVID-19 pandemic. Oximetry is widely used for respiration monitoring in the clinic, but it sometimes fails to capture a low-functional respiratory condition even though a patient has breathing difficulty. Another approach is breathing-sound monitoring, but this is unstable due to the indirect measurement of lung volume. Kobayashi in our team is developing a sensor measuring temporal changes in lung volume with a displacement sensor attached across the sixth and eighth ribs. For processing these respiratory signals, we propose the combination of complex-valued wavelet transform and the correlation among spectrum sequences. We present the processing results and discuss its feasibility to detect a low-functional condition in respiration. The result for detecting low-functional respiration showed good performance with a sensitivity of 0.88 and specificity of 0.88 to 1 in its receiver operating characteristic (ROC) curve.

On the Generation of Pi2 Pulsations due to Plasma Flow Patterns Around Magnetosheath Jets

AbstractWe report observations of a magnetosheath jet followed by a period of decelerated background plasma. During this period, THEMIS‐A magnetometer showed abrupt disturbances which, in the wavelet spectrum, appeared as prominent and irregular pulsations in two frequency bands (7.6–9.2 and 12–17 mHz) within the Pi2 range. The observations suggest—for the first time to our knowledge—that these pulsations were locally generated by the abrupt magnetic field changes driven by the jet’s interaction with the ambient magnetosheath plasma. Furthermore, similar pulsations, detected by THEMIS‐D inside the magnetosphere with a 140 s time‐lag (which corresponds to the propagation time of a disturbance traveling with Alfvénic speed), are shown to be directly associated with the ones in the magnetosheath, which raises the question of how exactly these pulsations are propagated through the magnetopause.

Study of Rail Squat Characteristics through Analysis of Train Axle Box Acceleration Frequency

In this study, a method for detecting the railway surface defects called “squats” using the ABA (Axle Box Acceleration) measurement of trains was proposed. ABA prototype design, implementation, and field tests were conducted to derive and verify the results. The field test was performed using a proven precision measurement system, and the measured data were signal-processed using a Matlab program. The algorithm used to determine the position of the squats was developed based on wavelet spectrum analysis. This study was verified for a section of a domestic general line and, following field verification for the section, squats was detected with a hit rate of about 88.2%. The main locations where the squats occurred were the rail welds and the joint section, and it was confirmed that in some sections, unsupported sleepers occurred at the locations where the squats occurred.

Вэйвлет анализ первой волны динамики заражения коронавирусом в Италии, Германии и Великобритании.

In this work, the wavelet spectra were calculated and analyzed for time series representing the dynamics of new daily cases of coronavirus infection in Italy, Germany and the UK. It was found that the Wavelet spectra for these countries have characteristic three different-scale internal cycles. It is shown that normalized graphs of the mean values of new daily cases of coronavirus infection have the same rate of increase and different rate of decrease.

The cold water mass along the southeast and east coasts of Korea in 2016–2017

The spatial and temporal behaviors and fluctuations of the cold water that appeared in the South East Sea and the East Sea coast from 2016 to 2017 were investigated. The water temperature drop was large in the east coast from April to June and the southeast coast from July to September, and the temperature drop period was longer in the southeast coast. The water temperature fluctuated sensitively to the wind direction, and it gradually decreased in the southwest wind but rose as if jumping in the northeast wind. Wind stress and surface water temperature had an inverse correlation, which was larger in Bukhang-Idukseo, and decreased toward the north of Guryongpo. The cold water appeared mainly in Geojedo-Pohang after 1 to 2 days when the southwest wind was strong, but when the wind became weak, it shrank to the Idukseo (Ulgi-Gampo) and extended into the open sea in a tongue shape. Cold water was distributed only in Samcheok-Toseong in mid-May, Idukseo-Guryongpo and Hupo-Jukbyeon-Samcheok from late May to mid-July, and Bukhang-Idukseo in August-September. The intensity of cold water was greatest in mid-August, and the center of cold water descended from the east coast to the southeast coast from spring to summer. The water temperature fluctuation was dominant at the periods of 1 d and 7–21 d. In wavelet spectrum analysis of water temperature and wind, wind speed increase-water temperature decrease showed phase difference of 12 h in 2 d, 18 h in 3 d, 1.5 d in 4–8 d, and 2–3 d in 8–24 d period. The correlation between the two parameters was large in Geojedo and Namhang, Bukhang-Idukseo, Guryongpo-Jukbyeon, and Samcheok-Toseong. Monitoring stations with high correlation in all periods were generally parallel to the monsoon direction.

Principal component analysis in the wavelet domain

This paper proposes a new principal component analysis method in the wavelet domain, which is useful for dimension reduction and feature extraction of multiple non-stationary time series. The proposed method is constructed using a novel combination of eigenanalysis and the local wavelet spectrum defined in the locally stationary wavelet process. Therefore, we can expect the proposed method to reflect a more generalized non-stationary time series beyond some limited types of signals that existing methods have performed. We investigate the theoretical results of estimated principal components and their loadings. The results of numerical examples, including the analysis of real seismic data and financial data, show the promising empirical properties of the proposed approach.

Fast magnetoacoustic wave trains: from tadpoles to boomerangs

ABSTRACT Rapidly propagating fast magnetoacoustic wave trains guided by field-aligned plasma non-uniformities are confidently observed in the Sun’s corona. Observations at large heights suggest that fast wave trains can travel long distances from the excitation locations. We study characteristic time signatures of fully developed, dispersive fast magnetoacoustic wave trains in field-aligned zero-β plasma slabs in the linear regime. Fast wave trains are excited by a spatially localized impulsive driver and propagate along the waveguide as prescribed by the waveguide-caused dispersion. In slabs with steeper transverse density profiles, developed wave trains are shown to consist of three distinct phases: a long-period quasi-periodic phase with the oscillation period shortening with time, a multiperiodic (peloton) phase in which distinctly different periods co-exist, and a short-lived periodic Airy phase. The appearance of these phases is attributed to a non-monotonic dependence of the fast wave group speed on the parallel wavenumber due to the waveguide dispersion, and is shown to be different for axisymmetric (sausage) and non-axisymmetric (kink) modes. In wavelet analysis, this corresponds to the transition from the previously known tadpole shape to a new boomerang shape of the wave train spectrum, with two well-pronounced arms at shorter and longer periods. We describe a specific previously published radio observation of a coronal fast wave train, highly suggestive of a change of the wavelet spectrum from a tadpole to a boomerang, broadly consistent with our modelling. The applicability of these boomerang-shaped fast wave trains for probing the transverse structuring of the waveguiding coronal plasma is discussed.

Wavelet and power spectrum analysis of global navigation satellite system multipath error modeling and mitigation

SummaryThis study investigates the multipath error modeling and mitigation for triple‐frequency global navigation satellite system (GNSS) signals inside South Korea. Multifrequency global positioning system (GPS), globalnaya navigatsionnaya sputnikovaya sistema (GLONASS), and Galileo data are collected in an environment where the receiver must track these three constellations in both low and high multipath scenarios. First, an advanced power spectrum analysis technique known as Welch method is performed using experimental data, and its benefits and drawbacks are described. In the second attempt, the spectrogram method is utilized to perform multipath feature time–frequency analysis. Although the abnormal frequency peak presented by the spectrogram is stable, the spectrogram does not support the precise recognition of the multipath error peak occurrence. Hence, in the third attempt, continuous wavelet transforms (CWT) are applied to highlight this type of peak resolution. The CWT function successfully indicated the maximum and minimum peak resolutions and exhibited a clear wavelet energy spread. In the final stage, experimental data are reconstructed by inverse CWT (ICWT), and comparative results in terms of root mean square before and after the ICWT are estimated. After implementing the inverse wavelet method in high and low multipath error of experimental data, overall average percentages of multipath mitigation reduction compared to actual multipath error are estimated to be 95.74% and 98.79%, respectively. This study demonstrates the high efficiency of the wavelet method as well as the effectiveness as a multipath error reduction approach. These improvements can be considered as significant in achieving high‐precision positioning accuracy.

Wavelet Spectra of a Chirped Gaussian Pulsed-Driven Harmonic Oscillator

We investigate the nature of spectral lines of emitted radiation due to of a non-dissipative single-mode quantized harmonic oscillator (HO) with train of n-chirped Gaussian pulses. Specifically, we analyze the transient emitted spectrum through two window wavelet functions of the radiation detector, namely the Haar wavelet and Morlet wavelet. Computational display of the exact analytical results shows how the driving pulse parameters (strength and number of pulses, chirping, repetition time) act as control knobs to shape the detected emitted spectrum as desired.

Prediction of leaf traits of lianas and trees via the integration of wavelet spectra in the visible-near infrared and thermal infrared domains

Predicting leaf traits using models based on spectroscopic data can provide essential information to advance ecological research and future Earth system models. Most current models are based on Partial Least Squares Regression (PLSR) algorithms that attempt to predict a set of leaf traits of several plant groups using leaf spectra. However, PLSR models tend to be inconsistent in describing the importance of absorption features when used to predict leaf traits. Likewise, the effect of contrasting absorption features of different plant groups on the prediction and evaluation of PLSR models is not well understood. Hence, this study focuses on using wavelet spectra to overcome current PLSR's limitation and improve leaf trait predictions. Specifically, we explored the use of visible–near-infrared (0.45–1.0 μm) and mid- long-wave infrared spectra (2.55–11 μm) to predict three-leaf traits of lianas and trees: Leaf Mass Area (LMA), Water Content (WC), and Equivalent Water Thickness (EWT). We also compare the effect of life forms on the prediction of traits by using sun leaves collected from 14 liana species and 21 tree species (n = 700) from a Neotropical Dry Forest. On each leaf, reflectance measurements were performed for both selected spectral regions; then, leaf traits were estimated from a leaf segment. Leaf reflectance was first resampled and then processed using continuous wavelet transformation (CWT) to derive the wavelet spectra. PLSR models linking the leaf traits and the reflectance or wavelet spectra were compared. Our results reveal that PLSR models based on wavelet spectra require fewer components to predict traits (13–16) than those based on reflectance (25–29). In addition, PLSR models' performance (e.g., R2) of testing datasets tend to be higher for models based on wavelet spectra (LMA = 0.83; WC = 0.77; EWT = 0.68) than reflectance (LMA = 0.78; WC = 0.76; EWT = 0.49). Wavelet spectra models also seem to better characterize absorption features that drive the variability of leaf traits than models based on reflectance. However, life forms play an essential role in model performance, where the prediction of lianas' traits presenting lower R2 (R2 = 0.61 ± 0.25) than trees' traits (R2 = 0.69 ± 0.15) regardless of the type of spectra or leaf trait. Our findings highlight the use of wavelet spectra to overcome limitations of the PLSR models for predicting leaf traits and the need to explore potential bias associated with plant groups on the model evaluations.

QPOs and Orbital elements of X-ray binary 4U 0115+63 during the 2017 outburst observed by Insight-HXMT

Abstract In this paper, we presented a detailed timing analysis of a prominent outburst of 4U 0115+63 detected by Insight-HXMT in 2017 August. The spin period of the neutron star was determined to be 3.61398 ± 0.00002 s at MJD 57978. We measured the period variability and extract the orbital elements of the binary system. The angle of periastron evolved with a rate of $0.048^\circ \pm 0.003^\circ \rm \, yr^{-1}$. The light curves are folded to sketch the pulse profiles in different energy ranges. A multi-peak structure in 1-10 keV is clearly illustrated. We introduced wavelet analysis into our data analysis procedures to study QPO signals and perform a detailed wavelet analysis in many different energy ranges. Through the wavelet spectra, we report the discovery of a QPO at the frequency ∼10 mHz. In addition, the X-ray light curves showed multiple QPOs in the period of ∼16 − 32 s and ∼67 − 200 s. We found that the ∼100 s QPO was significant in most of the observations and energies. There exist positive relations between X-ray luminosity and their Q-factors and S-factors, while the QPO periods have no correlation with X-ray luminosity. In wavelet phase maps, we found that the pulse phase of ∼67 − 200 s QPO drifting frequently while the ∼16 − 32 s QPO scarcely drifting. The dissipation of oscillations from high energy to low energy was also observed. These features of QPOs in 4U 0115+63 provide new challenge to our understanding of their physical origins.

Mid-term Periodicities in Solar Radio Emission Corresponding to Sunspot Number During Solar Cycle 23

We present a systematic time-series analysis of solar radio emission in nine different frequencies to compare with that of daily sunspot number (SSN) during Solar Cycle 23 (1996–2009). Owing to the contribution from quiet-sun emission, the total solar fluxes in microwaves do not decrease as significantly as the sunspot number does during 2006 to 2009. Lomb–Scargle (LS) and wavelet analysis techniques are employed to infer the various periodicities present in the time-series data. False alarm probability (FAP) levels are estimated by the use of background mean power spectrum in the global wavelet spectrum. The LS periodogram contains resolved period peaks, some of which are below FAP levels, for example a well-known rotational period. These peaks are assessed with global significance levels of the wavelet analysis. In all the data sets, the period for solar rotational modulation (26–31 days) is present. The periodogram for the SSN presents Rieger type periods (130–180 days), mid-term periods (300–400 days) and long-term periods (430–850 days). These periods in north and south are not similar, especially long term periods are missing in SSN data of the southern hemisphere. Corresponding to the SSN periodicities, Rieger and near Rieger type of oscillations (130–180 days), quasi-biennial periodicities in the range of 1.2 to 3 years were detected in the time-series data of radio frequencies. Several of these detected periods fall in the range of the periods that are suggested to be connected with magneto-Rossby wave spherical harmonics. Our analysis found reduced power levels in the LS periodograms of low frequencies because of the fact that these low frequency emissions originate higher up in the corona with diminishing contrast to small scale structures.

Transitional pulsatile flows with stenosis in a two-dimensional channel

Although blood flows are mostly laminar, transition to turbulence and flow separations are observed at curved vessels, bifurcations, or constrictions. It is known that wall-shear stress plays an important role in the development of atherosclerosis as well as in arteriovenous grafts. In order to help understand the behavior of flow separation and transition to turbulence in post-stenotic blood flows, an experimental study of transitional pulsatile flow with stenosis was carried out using time-resolved particle image velocimetry and a microelectromechanical systems wall-shear stress sensor at the mean Reynolds number of 1750 with the Womersley number of 6.15. At the start of the pulsatile cycle, a strong shear layer develops from the tip of the stenosis, increasing the flow separation region. The flow at the throat of the stenosis is always laminar due to acceleration, which quickly becomes turbulent through a shear-layer instability under a strong adverse pressure gradient. At the same time, a recirculation region appears over the wall opposite to the stenosis, moving downstream in sync with the movement of the reattachment point. These flow behaviors observed in a two-dimensional channel flow are very similar to the results obtained previously in a pipe flow. We also found that the behavior in a pulsating channel flow during the acceleration phase of both 25% and 50% stenosis cases is similar to that of the steady flow, including the location and size of post-stenotic flow separation regions. This is because the peak Reynolds number of the pulsatile flow is similar to that of the steady flow that is investigated. The transition to turbulence is more dominant for the 50% stenosis as compared to the 25% stenosis, as the wavelet spectra show a greater broadening of turbulence energy. With an increase in stenosis to 75%, the accelerating flow is directed toward the opposite wall, creating a wall jet. The shear layer from the stenosis bifurcates as a result of this, one moving with the flow separation region toward the upper wall and the other with the wall jet toward the bottom wall. Low wall-shear stress fluctuations are found at two post-stenotic locations in the channel flow – one immediately downstream of the stenosis over the top wall (stenosis side) inside the flow separation region, and the other in the recirculation region on the bottom wall (opposite side of the stenosis).

Spectral Analysis and Prediction of the Wave Forces Acting on Coastal Bridge Decks

The wave action on a box girder-type bridge deck is experimentally investigated in this study. Two types of incident waves, namely, regular waves (RWs) and focused waves (FWs), are tested. Fourier, wavelet, and Hilbert spectra of the vertical wave forces are obtained and analyzed. Four different methods are then applied to obtain the low- and high-frequency components of the total vertical wave force. Based on the separation results, the relationship between the wave force and wave crest amplitude is thereafter examined. An empirical formula is proposed to predict the vertical wave force. It is hoped that the aforementioned empirical formula may be widely applied during bridge design.

New inverse wavelet transform method with broad application in dynamics

Extracting multi-scale models from system identification of stationary or nonstationary measured signals (e.g., time series) is of great importance in engineering and the applied sciences. We propose a new computational method for harmonic analysis and decomposition of signals based on the inverse wavelet transform and demonstrate its efficacy in diverse areas in dynamics. The wavelet transform is a linear transformation of a signal measured in the temporal/spatial domain to the time–frequency/space-wavenumber domain and applies to stationary and nonstationary measurements. The new method is based on a numerical inverse wavelet transform and yields decomposition of the measured signal in terms of its dominant harmonic components. First, we formulate the analytical continuous inverse wavelet transform in a way that is suitable for computational implementation. Then, taking as example a general measured signal in the time domain, (i) we numerically compute its numerical wavelet transform spectrum, (ii) define a set of “harmonic regions” in the wavelet spectrum containing the dominant harmonics to be inverted and studied, and (iii) by numerically inverse wavelet transforming each of the harmonic regions separately, obtain the respective decomposed harmonics in the time domain. Note that, by construction, the superposition of all decomposed harmonics reconstructs the original signal. Next, we demonstrate the efficacy of the method with some examples. We start with an artificial signal with prescribed harmonic components to highlight the method and its accuracy. Then, we show applicability of the method to system identification, by applying it to the modal analysis of a system of linearly coupled oscillators with closely spaced modes. Lastly, we show how the new method enables quantification of the energy captured by each of the decomposed components (harmonics) in the response of a strongly nonlinear system. To this end, a single degree of freedom geometrically nonlinear oscillator is considered, and the method is used to quantify nonlinear energy “scattering” in its frequency domain. These examples hint at the broad applicability of the new method to diverse areas of signal processing and dynamics, including discrete and continuous dynamical systems with strongly (and even non-smooth) nonlinearities.

Uniform discrete wavelet spectrum for detection of hydrologic variability at multiple timescales

Detecting the signals of hydrologic variability, including both periodicities and trends, at multi-timescales with evaluation of their statistical significance is one of the primary goals in hydrology studies, but it is also a challenging task. While the discrete wavelet spectrum (DWS) has been widely used to meet this purpose, it has limitations in practical applications, especially with the difficulty in detecting the spatial heterogeneity in hydrologic variability. In this study, a uniform DWS method is developed by determining the spectral values of the reference DWS, which are used as a uniform criterion for significance evaluation to identify hydrologic signals and compare their spatial heterogeneity. Application of the uniform DWS method to three annual runoff (and the corresponding precipitation) time series in the Yarlung Tsangpo River basin indicates that the significance of the runoff variability increases from down- to up-streams. It is shown that the uncertainty becomes large when the variability at small timescales is considered in short hydrologic time series. It is also demonstrated that hydrologic variability at long timescales usually tends to have a non-monotonic trend and that a monotonic trend would misrepresent the true underlying behavior. The uniform DWS method proposed here, by identifying the periodicities, non-monotonic and monotonic trend with significance evaluation, has the potential for a much wider use in hydrologic and climate sciences.

Is Mesospheric Quasi Biennial Oscillation Ephemeral?

AbstractThe time evolution of mesospheric quasi biennial oscillation (MQBO) in the 82–98 km altitude region using long‐term meteor radar observations over low and equatorial latitudes and TIMED Doppler Interferometer (TIDI) observations is discussed for the first time. The wavelet spectra of monthly mean zonal winds over Serpog (6.4°S, 106.7°E; 1993–1998), Koto Tabang (0.2°S, 100.3°E; 2003–2012) and Thumba (8.5°N, 76.9°E; 2006–2015) show the transient nature of the MQBO amplitudes, thus, questioning its perpetuity in the mesosphere‐lower thermosphere (MLT). The time period of the MQBO as well as its amplitude show variability with time. The latitude‐height structures of the MQBO at four time periods (24, 26, 28, and 30 months) are constructed using TIDI measurements, which show diverse latitudinal structure. The significance of the present study lies in bringing out the time evolution of the MQBO and addressing a few outstanding issues on its ephemerality and discrepancies in its amplitudes.

Вейвлет-анализ динамики волн заражения коронавирусом во Франции, Швеции и Китае.

In this work, the wavelet spectra were calculated and studied for time series representing the dynamics of the new cases of coronavirus infection in France, Sweden and China. It was found that the Wavelet spectra for these countries have characteristic different-scale internal cycles, the number of which depends on the nature of the quarantine activities. It was detected that structure of the Wavelet spectra, their duration is practically independent of the geographic location, density and population size.

Detection of Concrete Structural Defects Using Impact Echo Based on Deep Networks

Abstract Deep learning is widely used in image processing, which significantly improves the performance of image classification detection. Based on the current status of concrete structure defect detection technology, this experimental study on the detection of concrete structure defects using impact echo was conducted. Focusing on the unsteady features of the impact echo signal, we adopted wavelet transforms at different scales to extract the wavelet spectrum. At the same time, the convolution and subsample operation were combined to establish the recognition system of concrete structure defect detection based on the deep learning network. The research results show that this system can accurately recognize defects in the concrete structure and has high detection accuracy in the concrete structure assessment process.

Application of fractal theory in diagnostics of composite materials

The article presents the results of studies to identify the features of diagnostic acoustic signals when defects are detected in composite materials using the methods of the theory of fractals. The use of the analysis of the spectral power density (PSD) and wavelet spectra of these signals did not lead to the detection of significant quantitative differences in the acoustic signals during the process of sample diagnostics (panel 4 mm thick). Acoustic signals from the standpoint of analyzing the characteristics of multifractal spectra were analyzed. It is shown that the defect state of the sample corresponds to the monofractal characteristic of the multifractal spectrum.