Time-varying Spectrum Research Articles

Dynamic Regimes of El Niño Southern Oscillation and Influenza Pandemic Timing.

El Niño southern oscillation (ENSO) dynamics has been shown to drive seasonal influenza dynamics. Severe seasonal influenza epidemics and the 2009–2010 pandemic were coincident with chaotic regime of ENSO dynamics. ENSO dynamics from 1876 to 2016 were characterized to determine if influenza pandemics are coupled to chaotic regimes. Time-varying spectra of southern oscillation index (SOI) and sea surface temperature (SST) were compared. SOI and SST were decomposed to components using the algorithm of noise-assisted multivariate empirical mode decomposition. The components were Hilbert transformed to generate instantaneous amplitudes and phases. The trajectories and attractors of components were characterized in polar coordinates and state space. Influenza pandemics were mapped to dynamic regimes of SOI and SST joint recurrence of annual components. State space geometry of El Niños lagged by influenza pandemics were characterized and compared with other El Niños. Timescales of SOI and SST components ranged from sub-annual to multidecadal. The trajectories of SOI and SST components and the joint recurrence of annual components were dissipative toward chaotic attractors. Periodic, quasi-periodic, and chaotic regimes were present in the recurrence of trajectories, but chaos–chaos transitions dominated. Influenza pandemics occurred during chaotic regimes of significantly low transitivity dimension (p < 0.0001). El Niños lagged by influenza pandemics had distinct state space geometry (p < 0.0001). Chaotic dynamics explains the aperiodic timing, and varying duration and strength of El Niños. Coupling of all influenza pandemics of the past 140 years to chaotic regimes of low transitivity indicate that ENSO dynamics drives influenza pandemic dynamics. Forecasts models from ENSO dynamics should compliment surveillance for novel influenza viruses.

Non-stationary random response analysis of structures with uncertain parameters

This paper proposes a non-stationary random response analysis method of structures with uncertain parameters. The structural physical parameters and the input parameters are considered as random variables or interval variables. By using the pseudo-excitation method and the direct differentiation method (DDM), the analytical expression of the time-varying power spectrum and the time-varying variance of the structure response can be obtained in the framework of first order perturbation approaches. In addition, the analytical expression of the first-order and second-order partial derivative (e.g., time-varying sensitivity coefficient) for the time-varying power spectrum and the time-varying variance of the structure response expressed via the uncertainty parameters can also be determined. Based on this and the perturbation technique, the probabilistic and non-probabilistic analysis methods to calculate the upper and lower bounds of the time-varying variance of the structure response are proposed. Finally the effectiveness of the proposed method is demonstrated by numerical examples compared with the Monte Carlo solutions and the vertex solutions.

Time-scaling vibrato tones while preserving vibrato rate

Elongation of vibrato tones while preserving vibrato rate is a non-trivial problem in audio processing. It is well known that linear time-scaling in the time domain simply translates duration in lockstep with pitch. In the time/frequency domain, frequencies are preserved under linear time-scaling, but vibrato rates are not. Looping can preserve rate, but there is a problem synchronizing loops with vibrato cycles. Our current method is to parameterize harmonic frequency- and amplitude-vs-time variations so that vibrato rate is one of the parameters, along with vibrato depth and frequency drift. A heterodyne/filter method, where the heterodyne frequency is estimated from an FFT of the full-duration frequency deviation waveform, is used for vibrato analysis. Harmonic amplitude vibrato parameters can be estimated either by using the heterodyne/filter method directly or by using amplitude-vs-frequency relationships. Once the model is completed, the harmonic parameters can be time-scaled while keeping the vibrato rate intact. An exception to this treatment is to keep the attack and decay epochs intact. Once recomputed, the new time-varying harmonic spectrum representation is converted to a time-domain signal via sinusoidal additive synthesis.

A nonparametric test for slowly-varying nonstationarities

This paper develops a new nonparametric method that is suitable for detecting slowly-varying nonstationarities that can be seen as trends in the time marginal of the time-varying spectrum of the signal. The rationale behind the proposed method is to measure the importance of the trend in the time marginal by using a proper test statistic, and further compare this measurement with the ones that are likely to be found in stationary references. It is shown that the distribution of the test statistic under stationarity can be modeled fairly well by a Generalized Extreme Value (GEV) pdf, from which a threshold can be derived for testing stationarity by means of a hypothesis test. Finally, the new method is compared with other ones found in the literature.

Designing high-resolution time–frequency and time–scale distributions for the analysis and classification of non-stationary signals: a tutorial review with a comparison of features performance

This paper deals with the problem of extracting information from non-stationary signals in the form of features that can be used for effective decision-making in both data analysis and machine learning for automatic classification systems. Suitable time–frequency (TF) and time–scale (TS) representations of such signals are reviewed for these purposes, and, the relationships between such TF and TS signal transformations is discussed. Both linear (atomic) decompositions and quadratic distributions are considered as well as other related methods such as fractional Fourier transform, polynomial Wigner–Ville distributions and time-varying order spectra. Current state-of-the-art methods are reviewed, and new results are presented including extensions of existing methods.Machine learning methodologies using TF/TS features can result in the design of systems that improve the classification of non-stationary signals. Using selected TF distributions (TFDs) and TS distributions (TSDs), the extraction of such TF/TS features is demonstrated on multi-channel recordings using channel fusion or feature fusion approaches. Extending the findings of previous studies, a TF/TS feature set is formed by including two complementary categories: signal related features and image features. The design of high-resolution TF/TS algorithms is then refined to account for issues of accuracy and robustness. Then, the desired TF/TS features are selected using different feature selection algorithms and compared with respect to the classification performance. Finally, other features from related methods are added, and comparisons performed. Improvements of up to 5% are obtained when using the chosen feature set after wrapper feature selection with channel feature fusion.

Modeling of DMSP Surface Charging Events

Measured spectra from a selection of Defense Meteorological Satellite Program-observed charging events were analyzed, with the goal of improving modeling of auroral charging events. Each data set was examined for correlations between the chassis potential and the measured fluxes. Chassis potential was found to be correlated with both the median electron energy and the net electron flux. The background plasma density cannot be determined directly from the measured spectra due to distortions from charging and the variation in sensitivity with incident particle energy across each energy channel. Simulations using time-varying spectra show that the chassis potential responds to even fairly subtle environment changes on a millisecond time scale. As the environment measurements take 1 s per spectrum, the chassis potential can easily be changing, either steadily or erratically, during that time. Once the limitations of the measurements are accounted for, the calculated chassis potential agrees with the measured potential through the modeled charging events.

Conditional adaptive Bayesian spectral analysis of nonstationary biomedical time series.

Many studies of biomedical time series signals aim to measure the association between frequency-domain properties of time series and clinical and behavioral covariates. However, the time-varying dynamics of these associations are largely ignored due to a lack of methods that can assess the changing nature of the relationship through time. This article introduces a method for the simultaneous and automatic analysis of the association between the time-varying power spectrum and covariates, which we refer to as conditional adaptive Bayesian spectrum analysis (CABS). The procedure adaptively partitions the grid of time and covariate values into an unknown number of approximately stationary blocks and nonparametrically estimates local spectra within blocks through penalized splines. CABS is formulated in a fully Bayesian framework, in which the number and locations of partition points are random, and fit using reversible jump Markov chain Monte Carlo techniques. Estimation and inference averaged over the distribution of partitions allows for the accurate analysis of spectra with both smooth and abrupt changes. The proposed methodology is used to analyze the association between the time-varying spectrum of heart rate variability and self-reported sleep quality in a study of older adults serving as the primary caregiver for their ill spouse.

Time-varying demodulation analysis for rolling bearing fault diagnosis under variable speed conditions

Rolling bearings often work under variable speed conditions, resulting in nonstationary vibrations. How to effectively extract the time-varying fault frequency from nonstationary vibration signals is a key issue in rolling bearing fault diagnosis. To address this issue, a quality time–frequency analysis of excellent time–frequency readability and robust to noise is necessary. To this end, the concentration of frequency and time (ConceFT) method is exploited. Based on this time–frequency analysis method, and considering the modulation feature of rolling bearing vibrations, we propose joint time-varying amplitude and frequency demodulated spectra to reveal the time-varying fault characteristic frequency. Firstly, the optimal frequency band sensitive to rolling bearing fault is selected by spectral kurtosis. Then, both the amplitude envelope and instantaneous frequency of the sensitive signal component within the selected optimal frequency band are calculated. Next, the ConceFT method is applied to the amplitude envelope and instantaneous frequency to generate the time-varying amplitude and frequency demodulated spectra. Finally, rolling bearing fault can be diagnosed by analysis of the time-varying frequency revealed by the time-varying demodulated spectra. This method is free from complex time-varying sidebands, and is robust to noise interference. It is illustrated by numerical simulated signal analysis, and is further validated via lab experimental rolling bearing vibration signal analyses. The localized defects on both inner and outer race are successfully diagnosed.

Long memory and changepoint models: a spectral classification procedure

Time series within fields such as finance and economics are often modelled using long memory processes. Alternative studies on the same data can suggest that series may actually contain a ‘changepoint’ (a point within the time series where the data generating process has changed). These models have been shown to have elements of similarity, such as within their spectrum. Without prior knowledge this leads to an ambiguity between these two models, meaning it is difficult to assess which model is most appropriate. We demonstrate that considering this problem in a time-varying environment using the time-varying spectrum removes this ambiguity. Using the wavelet spectrum, we then use a classification approach to determine the most appropriate model (long memory or changepoint). Simulation results are presented across a number of models followed by an application to stock cross-correlations and US inflation. The results indicate that the proposed classification outperforms an existing hypothesis testing approach on a number of models and performs comparatively across others.

Improvement of and Parameter Identification for the Bimodal Time-Varying Modified Kanai-Tajimi Power Spectral Model

Based on the Kanai-Tajimi power spectrum filtering method proposed by Du Xiuli et al., a genetic algorithm and a quadratic optimization identification technique are employed to improve the bimodal time-varying modified Kanai-Tajimi power spectral model and the parameter identification method proposed by Vlachos et al. Additionally, a method for modeling time-varying power spectrum parameters for ground motion is proposed. The 8244 Orion and Chi-Chi earthquake accelerograms are selected as examples for time-varying power spectral model parameter identification and ground motion simulations to verify the feasibility and effectiveness of the improved bimodal time-varying modified Kanai-Tajimi power spectral model. The results of this study provide important references for designing ground motion inputs for seismic analyses of major engineering structures.

Efficient methodology for electrocardiogram beat classification

Electrocardiogram (ECG) beat behaves as a non-linear and non-stationary signal. Since most of the existing data processing tools are poor alternatives for processing such signals, Hilbert–Huang transform (HHT) proves to be an efficient method as it deals with a time-varying frequency spectrum. In this study, a new and efficient methodology is proposed using HHT for feature selection which includes a set of essential features such as weighted mean frequency, Kolmogorov complexity and other statistical features (median, standard deviation, kurtosis, skewness and central moment) computed from the intrinsic mode functions extracted using the empirical mode decomposition (EMD) algorithm. Further, one-against-one multi-class support vector machine is employed for the classification of six generic ECG beats, namely: normal, left bundle branch block, right bundle branch block, premature ventricular contraction, paced beat and atrial premature beat. The classification process in this study yields better results than existing methodologies in terms of classification accuracy equal to 99.51% along with sensitivity, specificity and positive predictivity of 98.64, 99.77 and 98.17%, respectively.

Adaptive spectral estimation for nonstationary multivariate time series

Following the nonstationary univariate time series model of Rosen et al. (2012), we propose an adaptive estimation of time-varying spectra and cross-spectra for analyzing possibly nonstationary multivariate time series. Under the Bayesian framework, the estimation is implemented by smoothing stochastic approximation Monte Carlo (SSAMC) methods. We show by simulation study that the proposed method achieves good performance for time series whether changing abruptly or smoothly. The superiority to the other existing methods is also investigated. An application to longitudinal vibration data of the containership provides a wave-approach angle range, which should be recommended when sailing under a harsh sea condition.

William J. Strong's musical instrument models

After studying acoustics with Harvey Fletcher at Brigham Young University (BYU) in the 1950s, Bill joined the computer music sound analysis/synthesis group led by Melville Clark, Jr., at the Massachusetts Institute of Technology in 1959. He presented his first musical acoustics paper, on clarinet tone synthesis, at the fall, 1964 ASA meeting in Austin. This was followed by a paper on oboe synthesis at the spring, 1965 meeting in Washington. These papers were elaborated on in two wind instrument synthesis papers he and Clark published in JASA in 1967. The pioneering method was called spectral envelope synthesis, although temporal envelope functions were also incorporated in the model. Parameters for this complex synthesis method were obtained from time-variant spectrum analyses done by David Luce (Ph.D. thesis, MIT, 1963). Later back at BYU, in the late 1970s and 1980s, Bill and his students began analyzing acoustic structures of wind instruments, culminating with Michael Thompson (M.S. thesis, BYU, 2000) and Bill publishing results on measurement and simulation of nonlinear propagation in a trombone in JASA in 2001. This clearly demonstrated that nonlinear propagation of waveforms in a pipe can produce very significant effects on the “brassiness” of a brass instrument’s output sound.

Parametric Study on Gold Nanoparticle Synthesis Using Aqueous Elaise Guineensis (Oil palm) Leaf Extract: Effect of Precursor Concentration

In this study, gold nanoparticles (AuNPs) were synthesized by using aqueous extract of Elaise guineensis (oil palm) leaves without addition of any external stabilizing agent. Effects of precursor concentrations (0.51 mM- 4.055mM) on SPR absorbance and AuNP particle size distribution were investigated. The synthesis reaction was monitored by measuring time-variant SPR spectrum of the reaction medium with a UV-vis spectrophotometer. Biosynthesized AuNPs were characterized using TEM, DLS, UV-vis and FTIR spectroscopy. TEM image analysis showed formation of predominantly spherical gold nanoparticles with mean particle diameter of 27.89±14.59nm were formed using 1.53mM gold concentration. DLS data showed that AuNPs with hydrodynamic diameter 55.22 ± 42.86nm were formed, indicating formation of multilayer coatings of biomolecules present in the leaf extract on nanoparticles. Spherical, triangular, pentagonal and hexagonal gold nanoparticles with mean particle diameter 22.88 ±8.21nm were formed when higher gold (III) precursor concentrations (4.055mM) were used. FTIR analysis revealed that carboxylic and phenolic compounds present in leaf extract played dual roles as reducing and stabilizing agents during synthesis of AuNPs.

Defocus and numerical focusing in interference microscopy with wide time-varying spectrum of illumination field

This paper presents an analysis of the influence of illumination with wide temporal spectrum on the properties of a defocused interference signal and numerically focused imaging in interference microscopy. It is shown that the differences in defocus influence on different spectral components of a signal with wide temporal spectrum may lead to degradation of the images of defocused sample parts, in spite of the use of numerical focusing. The magnitude of these effects depends on the temporal spectrum width, the numerical aperture of the imaging system and the amount of defocus. The influence of these effects on the properties of numerically focused imaging in Fourier domain optical coherence tomography/microscopy is considered.

A Novel Time-Varying Spectral Filtering Algorithm for Reconstruction of Motion Artifact Corrupted Heart Rate Signals During Intense Physical Activities Using a Wearable Photoplethysmogram Sensor.

Accurate estimation of heart rates from photoplethysmogram (PPG) signals during intense physical activity is a very challenging problem. This is because strenuous and high intensity exercise can result in severe motion artifacts in PPG signals, making accurate heart rate (HR) estimation difficult. In this study we investigated a novel technique to accurately reconstruct motion-corrupted PPG signals and HR based on time-varying spectral analysis. The algorithm is called Spectral filter algorithm for Motion Artifacts and heart rate reconstruction (SpaMA). The idea is to calculate the power spectral density of both PPG and accelerometer signals for each time shift of a windowed data segment. By comparing time-varying spectra of PPG and accelerometer data, those frequency peaks resulting from motion artifacts can be distinguished from the PPG spectrum. The SpaMA approach was applied to three different datasets and four types of activities: (1) training datasets from the 2015 IEEE Signal Process. Cup Database recorded from 12 subjects while performing treadmill exercise from 1 km/h to 15 km/h; (2) test datasets from the 2015 IEEE Signal Process. Cup Database recorded from 11 subjects while performing forearm and upper arm exercise. (3) Chon Lab dataset including 10 min recordings from 10 subjects during treadmill exercise. The ECG signals from all three datasets provided the reference HRs which were used to determine the accuracy of our SpaMA algorithm. The performance of the SpaMA approach was calculated by computing the mean absolute error between the estimated HR from the PPG and the reference HR from the ECG. The average estimation errors using our method on the first, second and third datasets are 0.89, 1.93 and 1.38 beats/min respectively, while the overall error on all 33 subjects is 1.86 beats/min and the performance on only treadmill experiment datasets (22 subjects) is 1.11 beats/min. Moreover, it was found that dynamics of heart rate variability can be accurately captured using the algorithm where the mean Pearson’s correlation coefficient between the power spectral densities of the reference and the reconstructed heart rate time series was found to be 0.98. These results show that the SpaMA method has a potential for PPG-based HR monitoring in wearable devices for fitness tracking and health monitoring during intense physical activities.

Constraints on Sensitivity to Auditory Modulation in the Perceptual Organization of Speech

Background/Study Context: The perception of speech requires the integration of sensory details from a rapidly fading trace of a time-varying spectrum. This effortful cognitive function has been difficult to assess. New tests measuring intelligibility of sine-wave replicas of speech provided an assay of this critical function in normal-hearing young adults.Methods: Four time-varying sinusoids replicated the frequency and amplitude variation of the natural resonances of spoken sentences. The temporal tolerance of perceptual integration of speech was measured by determining the effect on intelligibility of desynchronizing a single sine-wave component in each sentence. This method was applied in tests in which the sentences were temporally compressed or expanded over a 40% range.Results: Desynchrony was harmful to perceptual integration over a narrow temporal range, indicating that modulation sensitivity is keyed to a rate of 20 Hz. No effect of variation in speech rate was observed on the intelligibility measure, whether rate was accelerated or decelerated relative to the natural rate.Conclusion: Performance measures of desynchrony tolerance did not vary when speech rate was accelerated or decelerated, revealing constraints on integration that are arguably primitive, sensory, auditory, and fixed. Because these are not adaptable, they limit the potential for perceptual learning in this aspect of perceptual organization. Implications for describing the elderly listener are noted.

Analysis of dynamic SERS spectra measured with a nanoparticle during intracellular transportation in 3D

We observed intracellular transportation by using surface-enhanced Raman scattering (SERS) from gold nanoparticles moving in the cytosol. Simultaneous detection of the nanoparticle three-dimensional position and SERS spectra presents molecular vibrational modes and contains large amounts of information about bimolecular events. In order to determine the meaningful temporal spectral changes associated with specific intracellular events or functions, we analyzed the time series Raman spectra, considering both the motion of the gold nanoparticle and also the time-varying spectra, revealing that some molecular vibrational modes showed strong correlation with the gold nanoparticle motion. This type of time-space-spectrum variable analysis will enable us to visualize molecular dynamics such as dissociation of proteins in biological reactions. In particular, our approach enables us to study molecules which should be associated with the transportation process such as vesicle transport, nuclear entry and protein diffusion.

Wavelet-expansion-based stochastic response of chain-like MDOF structures

This paper presents a wavelet-expansion-based approach for response determination of a chain-like multi-degree-of-freedom (MDOF) structure subject to full non-stationary stochastic excitations. Specifically, the generalized harmonic wavelet (GHW) is first utilized as the expansion basis to solve the dynamic equation of structures via the Galerkin treatment. In this way, a linear matrix relationship between the deterministic response and excitation can be derived. Further, considering the GHW-based representation of the stochastic processes, a time-varying power spectrum density (PSD) relationship on a certain wavelet scale or frequency band between the excitation and response is derived. Finally, pertinent numerical simulations, including deterministic dynamic analysis and Monte Carlo simulations of both the response PSD and the story-drift-based reliability, are utilized to validate the proposed approach.

Wavelet analysis of wall turbulence to study large-scale modulation of small scales

Wavelet analysis is employed to examine amplitude and frequency modulations in broadband signals. Of particular interest are the streamwise velocity fluctuations encountered in wall-bounded turbulent flows. Recent studies have shown that an important feature of the near-wall dynamics is the modulation of small scales by large-scale motions. Small- and large-scale components of the velocity time series are constructed by employing a spectral separation scale. Wavelet analysis of the small-scale component decomposes the energy in joint time–frequency space. The concept is to construct a low-dimensional representation of the small-scale time-varying spectrum via two new time series: the instantaneous amplitude of the small-scale energy and the instantaneous frequency. Having the latter in a time-continuous representation allows a more thorough analysis of frequency modulation. By correlating the large-scale velocity with the concurrent small-scale amplitude and frequency realizations, both amplitude and frequency modulations are studied. In addition, conditional averages of the small-scale amplitude and frequency realizations depict unique features of the scale interaction. For both modulation phenomena, the much studied time shifts, associated with peak correlations between the large-scale velocity and small-scale amplitude and frequency traces, are addressed. We confirm that the small-scale amplitude signal leads the large-scale fluctuation close to the wall. It is revealed that the time shift in frequency modulation is smaller than that in amplitude modulation. The current findings are described in the context of a conceptual mechanism of the near-wall modulation phenomena.