Spectral Density Function Research Articles

Chemical Exchange Rate Study by NMR CPMG Method

Analysis of the NMR CPMG method is presented that enables direct sampling of the spectral-density function of the chemical exchange processes. The approach is demonstrated on a solution of sucrose in water. The result confirms that the method can provide insight into the details of the dynamics of molecular conformations beyond a single-parameter description by an exchange rate. The results of the method are not limited to a single exchange process but can be of advantage if a large and potentially unknown number of exchange processes is contributing to the dynamics of a spin system.

Comparing CMIP6 Climate Model Simulations of Annual Global Mean Temperatures to a New Combined Data Product

AbstractA new statistical approach to validating climate models is introduced. First, five observational estimates of global mean surface temperature with estimated standard errors are combined into one data product, latent observed annual global temperature anomalies for the years 1880–2014, using a Bayesian hierarchical statistical approach. Summarizing these observed anomalies, estimates of smooth trend, levels of warming, and residual dependence as summarized by the spectral density function, are provided with simultaneous 95% credible bands. Then, corresponding estimates of smooth trend, levels of warming, and residual dependence are produced for sixth Climate Model Intercomparison Project (CMIP6) historical simulations analyzed at the annual global temperature anomaly scale, and compared to these bands. Among our results, we find that 93 out of the 318 CMIP6 historical model runs contain trends fitting inside the simultaneous bands for the smooth trend constructed from the data products, and for residual temporal dependence 69 out of 318 model runs contain spectral density functions that are within the corresponding data‐product‐based‐bands. We estimate the mean global temperature increase from 1995–2014 relative to 1880–1899, from the data product, to be 0.896°C with a 95% credible interval of between 0.877 and 0.915. We find that 14 CMIP6 model runs agree with this interval, 197 model runs lead to a smaller temperature increase globally, and 107 model runs lead to a larger temperature increase.

Dynamic analysis of damping structures considering support stiffness

An analysis method for the random seismic response of viscoelastic damper structures with support is proposed. This method considers the influence of support stiffness and analyzes the dynamic characteristics associated with support stiffness. It also combines the advantages of the complex modal method (CMM) and the pseudo-excitation method (PEM), improving the complex integration operation in calculating the spectral moments and variances of random seismic responses. The support and the viscoelastic damper constitute the equivalent damper. The damper's constitutive relationship and structural dynamic equations are decoupled to calculate conveniently the frequency domain solution of the responses. Second, the quadratic decomposition of the power spectral density function (QD-PSDF) is applied to simplify the power spectrum and obtain the closed-form solution of spectral moments and variances. Finally, the structural dynamic characteristics and the influence of support stiffness on the vibration control effect of the equivalent damper are investigated based on the closed-form solution. The structural dynamic reliability is also discussed according to the first excursion failure criterion. The results demonstrate that the damper's control effect and structural reactions are reduced, while the dynamic reliability is also enhanced when increasing support stiffness. The performance of the structure and damper tends to stabilize when the support coefficient reaches a specific level.

Simulations and theory of power spectral density functions for time-dependent and anharmonic Langevin oscillators.

Simulations and theory are presented for the power spectral density functions (PSDs) of particles in time-dependent and anharmonic potentials, including the effects of a thermal environment leading to damping and fluctuating forces. We investigate three one-dimensional perturbations to the harmonic oscillator of which two are time-dependent changes in the natural frequency of the oscillator, while the other is a time-independent extension of the quadratic potential to include a quartic term. We investigate the effect of these perturbations on two PSDs of the motion that are used in experiments on trapped nano-oscillators. We also derive and numerically test the PSDs for the motion of a spherical nanoparticle in a Paul trap. We found that the simple harmonic Langevin oscillator's PSDs are good approximations for the x and y coordinates' PSDs for small values of the parameter q of the Mathieu equation, but the difference can be more than a factor of two as "q" increases. We also numerically showed that the presence of a permanent electric dipole on the nanosphere can significantly affect the PSDs in the x and y coordinates.

Delta Method Confidence Intervals for Linear Regression Processes With Long-memory Disturbances

This paper provides third and fourth-order coverage probability errors of delta method confidence intervals (CIs) for the covariance parameters of a time series generated by a linear regression model with strongly dependent errors. The CIs are based on the plug-in maximum likelihood (PML) estimators. Bounds have been established on the coverage probability errors of one-and two-sided delta method CIs based on the plug-in log-likelihood (PLL) function under some sets of conditions on the regression coefficients, the spectral density function, and the parameter values. It is shown that the the fourth order delta method CIs in the case of linear regression model with Gaussian, stationary and strongly dependent errors have coverage probability errors of O(n^-1) and that of the third-order has errors of O(n^-1/2) which is the same order of magnitude asymptotically as in the independent and identically distributed (iid) case.

Spiral drawing deficits in children with prenatal alcohol exposure.

Empirical investigations reveal that, in comparison to their typically developing peers, children with histories of prenatal alcohol exposure experience deficits in writing but not drawing skills,both of which require fine motor control. This study examines drawing skills in this clinical group by assessing simple free-form spiral drawings with indices of spectral features and structural organization. Children with (n = 15) and without (n = 24) prenatal alcohol exposure used their dominant and nondominant hands to draw a series of spirals using a wireless pen stylus that either provided concurrent visual feedback in the form of a black ink trace or left no visible ink trace of each drawing. Spirals were drawn on a sheet of paper placed on a digitizing table, which facilitated online data acquisition. The data were assessed by power spectral density function analysis and sample entropy analysis. In comparison to their typically developing peers, children with prenatal alcohol exposure produced spirals with a lower mean frequency and less spectral variability. Spirals in the prenatally exposed group were also lower in complexity and structural organization than in the control group. These results occurred independently of hand dominance or the availability of visual feedback. The drawing skills of children with prenatal alcohol exposure have inherent signal characteristics that differ significantly from those produced by typically developing peers. Simple tasks requiring fine motor control may be useful in identifying individuals with fetal alcohol spectrum disorders.

Comprehensive analysis of relaxation decays from high-resolution relaxometry

Relaxometry consists in measuring relaxation rates over orders of magnitude of magnetic fields to probe motions of complex systems. High-resolution relaxometry (HRR) experiments can be performed on conventional high-field NMR magnets equipped with a sample shuttle. During the experiment, the sample shuttle transfers the sample between the high-field magnetic center and a chosen position in the stray field for relaxation during a variable delay, thus using the stray field as a variable field. As the relaxation delay occurs outside of the probe, HRR experiments cannot rely on the control of cross-relaxation pathways, which is standard in high-field relaxation pulse sequences. Thus, decay rates are not pure relaxation rates, which may impair a reliable description of the dynamics. Previously, we took into account cross-relaxation effects in the analysis of high-resolution relaxometry data by applying a correction factor to relaxometry decay rates in order to estimate relaxation rates. These correction factors were obtained from the iterative simulation of the relaxation decay while the sample lies outside of the probe and a preceding analysis of relaxation rates which relies on the approximation of a priori multi-exponential decays by mono-exponential functions. However, an analysis protocol matching directly experimental and simulated relaxometry decays should be more self consistent and more generally applicable as it can accommodate deviations from mono-exponential decays. Here, we introduce Matching INtensities for the Optimization of Timescales and Amplitudes of motions Under Relaxometry (MINOTAUR), a framework for the analysis of high-resolution relaxometry that takes as input the intensity decays at all fields. This approach uses the full relaxation matrix to calculate intensity decays, allowing complex relaxation pathways to be taken into account. Therefore, it eliminates the need for a correction of decay rates and for fitting multi-exponential decays with mono-exponential functions. The MINOTAUR software is designed as a flexible framework where relaxation matrices and spectral density functions corresponding to various models of motions can be defined on a case-by-case basis. The agreement with our previous analyses of protein side-chain dynamics from carbon-13 relaxation is excellent, while providing a more robust analysis tool. We expect MINOTAUR to become the tool of choice for the analysis of high-resolution relaxometry.

Extending the Experimentally Accessible Range of Spin Dipole-Dipole Spectral Densities for Protein-Cosolute Interactions by Temperature-Dependent Solvent Paramagnetic Relaxation Enhancement Measurements.

Longitudinal (Γ1) and transverse (Γ2) solvent paramagnetic relaxation enhancement (sPRE) yields field-dependent information in the form of spectral densities that provides unique information related to cosolute-protein interactions and electrostatics. A typical protein sPRE data set can only sample a few points on the spectral density curve, J(ω), within a narrow frequency window (500 MHz to ∼1 GHz). However, complex interactions and dynamics of paramagnetic cosolutes around a protein make it difficult to directly interpret the few experimentally accessible points of J(ω). In this paper, we show that it is possible to significantly extend the experimentally accessible frequency range (corresponding to a range from ∼270 MHz to 1.8 GHz) by acquiring a series of sPRE experiments at different temperatures. This approach is based on the scaling property of J(ω) originally proposed by Melchior and Fries for small molecules. Here, we demonstrate that the same scaling property also holds for geometrically far more complex systems such as proteins. Using the extended spectral densities derived from the scaling property as the reference dataset, we demonstrate that our previous approach that makes use of a non-Lorentzian Ansatz spectral density function to fit only J(0) and one to two J(ω) points allows one to obtain accurate values for the concentration-normalized equilibrium average of the electron-proton interspin separation ⟨r-6⟩norm and the correlation time τC, which provide quantitative information on the energetics and timescale, respectively, of local cosolute-protein interactions. We also show that effective near-surface potentials, ϕENS, obtained from ⟨r-6⟩norm provide a reliable and quantitative measure of intermolecular interactions including electrostatics, while ϕENS values obtained from only Γ1 or Γ2 sPRE rates can have significant artifacts as a consequence of potential variations and changes in the diffusive properties of the cosolute around the protein surface. Finally, we discuss the experimental feasibility and limitations of extracting the high-frequency limit of J(ω) that is related to ⟨r-8⟩norm and report on the extremely local intermolecular potential.

Binary Neutron-Star Mergers with a Crossover Transition to Quark Matter

This paper summarizes recent work on the possible gravitational-wave signal from binary neutron-star mergers in which there is a crossover transition to quark matter. Although this is a small piece of a much more complicated problem, we discuss how the power spectral density function may reveal the presence of a crossover transition to quark matter.

GARTFIMA process and its empirical spectral density based estimation

ABSTRACT In this article, we introduce a Gegenbauer autoregressive tempered fractionally integrated moving average process. We work on the spectral density and autocovariance function for the introduced process. The parameter estimation is done using the empirical spectral density with the help of the nonlinear least square technique and the Whittle likelihood estimation technique. The performance of the proposed estimation techniques is assessed on simulated data. Further, the introduced process is shown to better model the real-world data in comparison to other time series models.

Uncertainty Propagation of Missing Data Signals with the Interval Discrete Fourier Transform

The interval discrete Fourier transform (DFT) algorithm can propagate signals carrying interval uncertainty. By addressing the repeated variables problem, the interval DFT algorithm provides exact theoretical bounds on the Fourier amplitude and estimates of the power spectral density (PSD) function while running in polynomial time. Thus, the algorithm can be used to assess the worst-case scenario in terms of maximum or minimum power, and provide insights into the amplitude spectrum bands of the transformed signal. To propagate signals with missing data, an upper and lower value for the missing data present in the signal must be assumed, such that the uncertainty in the spectrum bands can also be interpreted as an indicator of the quality of the reconstructed signal. For missing data reconstruction, there are a number of techniques available that can be used to obtain reliable bounds in the time domain, such as Kriging regressors and interval predictor models. Alternative heuristic strategies based on variable—as opposed to fixed—bounds can also be explored. This work aims to investigate the sensitivity of the algorithm against interval uncertainty in the time signal. The investigation is conducted in different case studies using signals of different lengths generated from the Kanai-Tajimi PSD function, representing earthquakes, and the Joint North Sea Wave Observation Project (JONSWAP) PSD function, representing sea waves as a narrowband PSD model.

VECTOR <i>S</i>-PARAMETRIC ANALYSIS OF SIGNAL PHASE DYNAMIC RADIO IMAGES

A vector method for recording phase-dynamic radio images is proposed by forming and numerically analyzing the S-parametric scattering matrix of multidisciplinary signatures of material media and objects. The key advantages of aperture capture of signal radio images by the method of frequency-synthesized power spectral density function of a scattered wave radio profile are determined. On the basis of a vector analyzer of microwave circuits and broadband antennas of the Vivaldi type, an experimental laboratory installation for signal registration of time-scale radio images in the spectral region of 0.03…6.0 GHz has been built. The dependences of the influence of the angular characteristics of the object on the spectral-temporal structure of the formation of phase-dynamic radio images have been experimentally established. As a time-scale postprocessing of radio images, a method of cepstral transformation of S-parametric characteristics with convolution of basic signatures in the radiogenic of the irradiated object is proposed. A series of cepstral convolutions of phase-dynamic radio images was obtained, establishing a functional relationship between the change of the signature of an object in time with its radio genome.

Duration and damping for ground motion characterization in frequency‐domain damage estimation of SDOF structures

AbstractIn estimating the damage to a single‐degree‐of‐freedom (SDOF) structure due to multiple earthquake events, it may be convenient to use a frequency‐based approach, in which the anticipated ground motions are characterized through power spectral density functions (PSDFs) compatible with the specified design spectra for those motions. Since a spectrum‐compatible PSDF corresponds to a fictitious stationary ground motion process of a specified duration, the duration of this process should preferably be same as the length of the stationary segment in the actual ground acceleration process for a meaningful computation of the stochastic response. On assuming the strong‐motion segment of a given ground motion to represent its stationary segment, the nonstationarity of the strong‐motion segment is evaluated for the existing strong‐motion duration definitions. It is found that the Trifunac‐Brady definition is the most reasonable strong‐motion duration definition in respect of consistently giving the longest strong‐motion segment with least nonstationarity. Further, a spectrum‐compatible PSDF can be used for estimating the stochastic response of a linear system, provided the system has the same damping ratio as that of the design spectrum from which the PSDF has been computed. This causes errors in estimating the peak response of an equivalent linear system due to its damping ratio being higher than the initial damping ratio of the nonlinear system. To address this, an empirical expression is developed for the modified damping ratio of a linear system, which would lead to the correct peak response of the system on using the PSDF obtained from the 5%‐damping design spectrum.

Laser Beam Quality of Airy Beam in the Jet Engine Exhaust Induced Turbulence

Theoretical predictions of laser beam interactions with jet-engine-exhaust-induced turbulence are of importance for optimization of various optical systems, including LIDARs and airborne laser measurement systems. This paper is based on the extended Huygens–Fresnel diffraction integral and the Wigner distribution function, combined with the recently proposed power spectral density function of atmospheric turbulence induced by jet engine exhaust, to derive the formula for the quality factor of a partially coherent Airy beam in turbulent media induced by jet engine exhaust. Numerical calculations based on the analytical formula show that the smaller the structure constant and outer scale of the atmospheric turbulence induced by jet engine exhaust, the smaller the quality factor of a partially coherent Airy beam, indicating better laser beam quality. At the same time, the larger the generalized parameter and inner scale of the jet-engine-exhaust-induced turbulence and the longer the wavelength of the laser beam, the smaller the corresponding quality factor. The numerical results also show that reducing the coherence length of a partially coherent Airy beam and increasing its characteristic width are beneficial for reducing the quality factor in the atmospheric turbulence induced by jet engines. However, the numerical results show that increasing the coherence length of a partially coherent Airy beam and reducing its characteristic width are beneficial for reducing the quality factor in vacuum. This situation demonstrates significant differences between the interaction mechanisms of an Airy beam in vacuum and in the jet-engine-exhaust-induced turbulence. The results of our discussion contribute to clarifying the mechanism of interaction between an Airy laser beam and random media, as well as the application of a curved Airy laser beam in practical situations.

Machine-Learning-Assisted Cyclostationary Spectral Analysis for Joint Signal Classification and Jammer Detection at the Physical Layer of Cognitive Radio.

Cognitive radio technology was introduced as a possible solution for spectrum scarcity by exploiting dynamic spectrum access. In the last two decades, most researchers focused on enabling cognitive radios for managing the spectrum. However, due to their intelligent nature, cognitive radios can scan the radio frequency environment and change their transmission parameters accordingly on-the-fly. Such capabilities make it suitable for the design of both advanced jamming and anti-jamming systems. In this context, our work presents a novel, robust algorithm for spectrum characterisation in wideband radios. The proposed algorithm considers that a wideband spectrum is sensed by a cognitive radio terminal. The wideband is constituted of different narrowband signals that could either be licit signals or signals jammed by stealthy jammers. Cyclostationary feature detection is adopted to measure the spectral correlation density function of each narrowband signal. Then, cyclic and angular frequency profiles are obtained from the spectral correlation density function, concatenated, and used as the feature sets for the artificial neural network, which characterise each narrowband signal as a licit signal with a particular modulation scheme or a signal jammed by a specific stealthy jammer. The algorithm is tested under both multi-tone and modulated stealthy jamming attacks. Results show that the classification accuracy of our novel algorithm is superior when compared with recently proposed signal classifications and jamming detection algorithms. The applications of the algorithm can be found in both commercial and military communication systems.

Response spectrum method for structures subjected to vertical ground motions: Absolute acceleration method

AbstractAlthough a wide variety of response spectrum methods have been developed to estimate peak horizontal building responses, much less attention has been devoted to study the applicability of those methods for the vertical direction or to develop new methods to estimate peak vertical building responses. Vertical building responses can be significant for structures located close to the earthquake rupture, and for buildings with fundamental period of vibration within the range of most energy content of the vertical component of the ground motion (typically 0.05 to 0.15 s). The frequency content of the vertical component is significantly different to that in the horizontal components; thus, it is not clear if previous methods are applicable. We present a new alternative response spectrum analysis (RSA) method to estimate absolute accelerations in the vertical direction, which is a modified version of a previously studied modal combination rule developed for the horizontal components of motion. This formulation is derived based on the use of modal absolute accelerations, and we compare it to the traditional complete quadratic combination (CQC). In the proposed method, we develop simplified equations to estimate the necessary correlation coefficients for the vertical direction which are calibrated to fit empirical correlations computed from the vertical response of single degree of freedom systems subjected to a set of 90 vertical components of recorded ground motions. We also compute these correlations by using an improved power spectral density (PSD) function, which is as an enhanced version of the modified Kanai‐Tajimi PSD to represent the frequency content in the vertical direction which differs from that in the horizontal direction. To evaluate the proposed modal combination rule, we compare the RSA results to those obtained using response history analyses (RHA) of peak responses for a simplified model consisting of a prismatic bar fixed only at one end, as well as for 2D frames. We show that the proposed modal combination rule can estimate peak building responses with higher accuracy than the commonly used CQC modal combination rule, for any general building configuration at any structural location.

An effective method for modelling wireless communication systems

Statement of the problem. To describe the multipath propagation of radio signals using two models: the ray tracing method and the method of stochastic simulation. Let us consider the stochastic model as the most general one that allows to describe various scenarios and factors influencing signal propagation such as multipath, arrival time variance, distance loss, atmospheric conditions, etc. Under real-world conditions, channel variation does not follow a Gaussian distribution. Coloured non-Gaussian noise has to be taken into account in the design and modelling of the wireless communication system. The complexity of the stochastic channel modelling method is that the variation of PSD power spectral density function and PDF probability density function of a random variable are strongly related to each other. To remove the limitations of existing methods, the Gaussian random variable filtering method is used. But in contrast to the applied simulation techniques, we will use Global Search Optimization (GSE) algorithm. Objective. To investigate a possibility of generation of colored non-Gaussian noise which satisfies the specified requirements by the filtering method based on the global search optimization algorithm. Results. The method based on the global search optimization algorithm for generating colored non-Gaussian noise, which satisfies specified requirements of the Spectral Power Density function and the Probability Density function, is proposed. Numerical simulation results confirm its effectiveness. The advantage of the new method is that the complexity of calculating the required pre-distortion for the filter is replaced by a simple search method. Once the required coefficients are found, non-Gaussian noise generation can be accomplished by secondary filtering and inverse transform. Practical Significance. Compared to methods based on block structures or other analytical methods, the proposed method is more suitable for real-time wireless channel simulation.

An Efficient Multiplexing Technique For 5G Wireless Network: Analysis and Selection

The 5G cellular communication technology is intended to base on the present Long-TermEvolution (LTE) 4G networks with adopted features. Features of low power consumption and theconstant power level should be the major requirement for an efficient channel allocation method. In thisresearch work, an analysis was performed on multiplexing techniques: Orthogonal Frequency DivisionMultiplexing (OFDM), Generalized Frequency Division Multiplexing (GFDM), Universal FilteredMulticarrier (UFMC) and Filter-Bank Multicarrier (FBMC). Smooth power level had been analyzedaccording to Power Spectral Density (PSD) function vs normalized frequency using AWGN channelmodel. The simulation was done by MATLAB 2019 Simulink software for OFDM and GFDM that werefurther compared to existing results of UFMC and FBMC multiplexing techniques. Calculated power forOFDM and GFDM were 32.1mW and 40.23 µW respectively. Comparative results showed the bettersmooth power spectrum, micro-watt power consumption and better hardware configuration for GFDM.That’s why GFDM channel allocation method selection is one step ahead for the next generationmultiplexing technique

Bootstrap Probability Errors of the Whittle MLE for Linear Regression Processes with Strongly Dependent Disturbances

This paper determines bounds on the asymptotic orders of the coverage probability errors of parametric bootstrap confidence intervals (CIs) and tests for the covariance parameters of a time series generated by a regression model with Gaussian, stationary, and strongly dependent errors. The CIs and tests are based on the plug-in Whittle maximum
 likelihood (PWML) estimators. It is shown that, under some sets of conditions on the regression coefficients, the spectral density function, and the parameter values, the bounds on the coverage probability errors of symmetric two-sided and one-sided parametric bootstrap confidence intervals on the plug-in Whittle log-likelihood function are shown to be O(n^{-3/2}\ln{n}) and O(n^{-1}\ln{n}), respectively. Apart from the \ln{n} term, the magnitudes of the coverage probability errors of the one-sided bootstrap confidence intervals for our model is shown to be essentially the same as that of the independent and identically distributed (iid) data. The error for the two-sided confidence intervals is not as small as the error O(n^{-2}) that has been established for many confidence intervals in the literature, see Hall (1992), pp 102-108.

Limiting spectral distribution of stochastic block model

The stochastic block model (SBM) is an extension of the Erdős–Rényi graph and has applications in numerous fields, such as data analysis, recovering community structure in graph data and social networks. In this paper, we consider the normal central SBM adjacency matrix with [Formula: see text] communities of arbitrary sizes. We derive an explicit formula for the limiting empirical spectral density function when the size of the matrix tends to infinity. We also obtain an upper bound for the operator norm of such random matrices by means of the Stieltjes transform and random matrix theory.