Harmonic long-memory models

This paper proposes a method to design a real-time wind turbulence simulator. The objective of such a simulator is to make dynamical models more accurate in order to develop more robust controls, especially in the case of mechanical systems operating outdoors such as tracking antennas. The models used to generate a random wind speed are based on the wind spectral characteristics rather than time domain ones. Indeed, turbulence is a stochastic and non-stationary process corresponding to the short-term component of wind and therefore is difficult to model in time domain. Wind spectral characteristics are described by the power spectral density whose approximation is used in the real-time simulator to reproduce wind behavior. The von Kármán model is the most commonly used model to approximate the power spectral density of wind turbulence. However, this model was originally designed for aircraft, and therefore for high altitudes and moving systems. In our case, tracking antennas are used under different conditions: low altitude and slow moving systems. This makes the von Kármán model less precise in middle and high range frequency. Consequently, there is a need in more accurately modeling wind turbulence under these specific conditions. As von Karman’s model expression uses fractional calculus, other models with the same range of parameter number are proposed to better approximate the wind power spectral density by using Cole-Cole and Davidson-Cole fractional models. The idea is to use shaping filters issued from these more precise fractional models to generate realistic random wind speed turbulence from a random white noise input. These filters are approximated by rational functions and their parameters are tuned in the same way as those of the von Kármán model with the same inputs (mean speed, standard deviation and length scale). If a rational model is sought, a very high number of parameters (more than six times) is needed to have the same precision as our proposed fractional Cole-Cole model which has only four parameters. Finally, an accurate turbulence wind speed generator is proposed.

The heart rate variability (HRV) is a measure based on the time position of the electrocardiogram (ECG) R-waves. There is a discussion whether or not we can obtain the HRV pattern from blood pressure (BP). In this paper, we propose a method for estimating HRV from a BP signal based on a HIF algorithm and carrying out experiments to compare BP as an alternative measurement of ECG to calculate HRV. Based on the hypotheses that ECG and BP have the same harmonic behavior, we model an alternative HRV signal using a nonlinear algorithm, called heart instantaneous frequency (HIF). It tracks the instantaneous frequency through a rough fundamental frequency using power spectral density (PSD). A novelty in this work is to use fundamental frequency instead of wave-peaks as a parameter to estimate and quantify beat-to-beat heart rate variability from BP waveforms. To verify how the estimate HRV signals derived from BP using HIF correlates to the standard gold measures, i.e. HRV derived from ECG, we use a traditional algorithm based on QRS detectors followed by thresholding to localize the R-wave time peak. The results show the following: 1) The spectral error caused by misestimation of time by R-peak detectors is demonstrated by an increase in high-frequency bands followed by the loss of time domain pattern. 2) The HIF was shown to be robust against noise and nuisances. 3) By using statistical methods and nonlinear analysis no difference between HIF derived from BP and HRV derived from ECG was observed.

The performance of tissue imaging is improved by tissue harmonic imaging (THI) to expand and enhance the range and level of clinical diagnosis for many diseases. The separation based on High-pass filtering (S_HPF) is a commonly used method for extracting harmonic components from ultrasonic echo signals. However, the cut-off frequency, order and algorithm to realize a high-pass filter have a great influence on the separation accuracy of harmonic signals. In present study, a novel separation method (S_CEEMDAN) based on the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) algorithm is proposed for adaptively separating harmonic components from ultrasonic echo signals. First, we calculate the ensemble size of CEEMDAN adaptively based on the added noise level, and draw a sum of intrinsic mode functions (IMFs) from the ultrasonic echo signals by CEEMDAN. Then, the spectrum of each IMF is computed and evaluated, and the IMFs containing both fundamental and harmonic components are further decomposed by using the CEEMDAN algorithm. This separation process is end until all of IMFs have been divided into either fundamental or harmonic categories. Finally, the corresponding fundamental and harmonic echo signals are yielded by accumulating separately these two categories. In experiments, simulated ultrasonic echo signals with a center frequency of 3.5MHz are separated by the proposed S_CEEMDAN method, and the results are compared with those processed by S_HPF. The edge of the harmonic image by S_CEEMDAN marginally better defined than S_HPF. The indices for the harmonic signals separated by S_CEEMDAN and S_HPF, respectively, are as follows: the center frequencies of 6.66 MHz and 6.65 MHz, 3 dB bandwidths of 1.04 MHz and 1.05 MHz, 6 dB bandwidths of 1.59 MHz and 1.55 MHz, signal-to-noise ratios (SNRs) of 14.00 and 13.63, and image contrasts of 7.01 and 7.06. In conclusion, due to good adaptive characteristics, and lower reconstruction errors, the proposed S_CEEMD method is superior to S_HPF in the performance of spectral accuracy and harmonic imaging. This method could be potentially alternative to the current method for the ultrasonic harmonic separation.

This study presents new insights into sparse frequency waveform analysis and new waveform design methods. For a general radar waveform, the total ambiguity in its auto-correlation function (ACF) is equal to the total energy in its power spectral density (PSD) in the frequency domain. With this relationship, the total ambiguity in an ACF is found to be minimised when the corresponding PSD is uniformly distributed. This property is extended to the sparse frequency waveform by establishing the relationship between the optimal PSD and the minimum ambiguity in ACF. Based on this analysis, a new method of designing sparse frequency waveform with sidelobe constraint is proposed. The new method simultaneously optimises the sidelobe performance and the PSD performance through constrained non-linear optimisation. This is different from existing methods that compromise the performance of sidelobe to the performance of PSD in an ad-hoc manner by minimising the weighted sum of the total power in the stopbands and the total power in the sidelobe. The analysis and the design method have been extended to the case of multiple sparse frequency waveforms. Simulation studies are provided to demonstrate the effectiveness of the proposed new design methods.

Collagen change is a major feature in the photoaged human skin. Here, we present the use of intrinsic second harmonic generation (SHG) signal as a novel means to quantify collagen change with photoaging. We obtain the SHG images of the superficial dermis from ex vivo the cheek skin and the abdomen skin of eight patients aged 55-60 years. The results show that SHG signal can quantitatively reveal collagen change between normal and photoaged human skin in three dimensions. By comparing normal with photoaged dermis, there are significant differences in the collagen content and fine structure, providing substantial potential to be applied in vivo for the clinical diagnosis of human skin photoaging.

Intrinsic second harmonic generation (SHG) signals can be used to visualize the three-dimensional structure of cardiac and skeletal muscle with high spatial resolution. Fluorescence labeling of complementary sarcomeric proteins, e.g. actin, indicates that the observed SHG signals arise from the myosin filaments. Recently, the myosin rod domain or LMM - light meromyosin - has been reported to be the dominant source of this SHG signal. However, to date, mostly negative and indirect evidence has been presented to support this assumption. Here, we show, to our knowledge, the first direct evidences that strong SHG signals can be obtained from synthetic paracrystals. These rod shaped filaments are formed from purified LMM. SDS-PAGE protein analysis confirmed that the LMM crystals lack myosin head domains. Some regions of the LMM paracrystals produce a strong SHG signal whereas others did not. The SHG signals were recorded with a laser-scanning microscope (Leica SP2). A ps laser tuned to 880 nm was used to excite the sample through an 63x objective of 1.2 NA. In order to visualize the synthetic filaments - in addition to SHG imaging -, the LMM was labeled with the fluorescent marker 5-IAF. We were able to observe filaments of 1 to 50 μm in length and of up to 5 μm in diameter. In conclusion, we can show that the myosin rod domain (LMM) is a dominant source for intrinsic SHG signals. There seems, however, a signal dependence on the paracrystals' morphology. This dependence is being investigated.

This is the second part of a study to elucidate the local field effects on the nonlinear optical properties of p-nitroaniline (pNA) in three solvents of different multipolar character, that is, cyclohexane (CH), 1,4-dioxane (DI), and tetrahydrofuran (THF), employing a discrete description of the solutions. By the use of liquid structure information from molecular dynamics simulations and molecular properties computed by high-level ab initio methods, the local field and local field gradients on p-nitroaniline and the solvent molecules are computed in quadrupolar approximation. To validate the simulations and the induction model, static and dynamic (non)linear properties of the pure solvents are also computed. With the exception of the static dielectric constant of pure THF, a good agreement between computed and experimental refractive indices, dielectric constants, and third harmonic generation signals is obtained for the solvents. For the solutions, it is found that multipole moments up to two orders higher than quadrupole have a negligible influence on the local fields on pNA, if a simple distribution model is employed for the electric properties of pNA. Quadrupole effects are found to be nonnegligible in all three solvents but are especially pronounced in the 1,4-dioxane solvent, in which the local fields are similar to those in THF, although the dielectric constant of DI is 2.2 and that of the simulated THF is 5.4. The electric-field-induced second harmonic generation (EFISH) signal and the hyper-Rayleigh scattering signal of pNA in the solutions computed with the local field are in good to fair agreement with available experimental results. This confirms the effect of the "dioxane anomaly" also on nonlinear optical properties. Predictions based on an ellipsoidal Onsager model as applied by experimentalists are in very good agreement with the discrete model predictions. This is in contrast to a recent discrete reaction field calculation of pNA in 1,4-dioxane, which found that the predicted first hyperpolarizability of pNA deviated strongly from the predictions obtained using Onsager-Lorentz local field factors.

The variation of device characteristics is a challenge to present and future large-scale integrations. One of the origins of the variation is line width roughness (LWR). To facilitate the efforts to cope with LWR, we developed a method to accurately characterize LWR basing on the analysis of power spectral densities (PSDs). Because experimental PSDs are intrinsically discrete, we derive simple analytic formulas of the discrete PSDs by assuming that the autocorrelation function (ACF) exponentially decays with distance. The PSDs calculated by using the formulas agree excellently with experimentally obtained PSDs of photoresist LWR. From the result we find that the photoresist LWR of this study has a standard deviation of 2.5 nm and an exponentially-decaying autocorrelation function with a correlation length of 35 nm. Although the experimental PSDs inevitably contain a component produced by scanning-electron-microscope (SEM)-image noise, the two components of LWR and noise are separately determined by the method of this study. Due to this feature, the resultant variance of LWR is independent of the noise intensity. However, it is still important to reduce the noise component in order to maintain the accuracy of analysis especially in the case of LWR that has an unknown functional form of PSD. This is because even the PSDs that have different functional forms sometimes look alike in the presence of large noise. To reduce the noise effect, it is effective to average the SEM images perpendicularly to fine lines before edge detections. The procedure does not reduce the variance unlike averaging along the lines. The method of this study is applicable not only to LWR but also to other cases as far as the ACF exponentially decays with distance, or equivalently the spectral line shape is Lorentzian. Accordingly, it forms the basis for spectral analysis of most experimental results.

We present model light curves for accreting black hole candidates (BHCs) based on a recently proposed model for their spectro-temporal properties. According to this model, the observed light curves and aperiodic variability of BHCs are due to a series of soft photon injections at random (Poisson) intervals near the compact object and their reprocessing into hard radiation in an extended but nonuniform hot plasma corona surrounding the compact object. We argue that the majority of the timing characteristics of these light curves are due to the stochastic nature of the Comptonization process in the extended corona, whose properties, most notably its radial density dependence, are imprinted in them. We compute the corresponding power spectral densities (PSD), autocorrelation functions, time skewness of the light curves, and time lags between the light curves of the sources at different photon energies and compare our results to observation. Our model light curves compare well with observations, providing good fits to their overall morphology, as manifest by the autocorrelation and skewness functions. The lags and PSDs of the model light curves are also in good agreement with those observed (the model can even accommodate the presence of quasi-periodic oscillations). Finally, while most of the variability power resides at timescales approximately a few seconds, at the same time, the model allows also for shots of a few milliseconds in duration, in accordance with observation. We suggest that refinements of this type of model along with spectral and phase lag information can be used to probe the structure of this class of high-energy sources.

Infrared converters to visible range are in demand for creation of optoelectronic devices, infrared visualizers and other non-linear optical devices. In this work we study nonlinear optical properties of monodisperse SiO2 and Si/SiO2 spheres encapsulated into silicone films. The fabricated silicone films containing SiO2 spheres demonstrated a bright third harmonic generation signal, and films with Si/SiO2 spheres demonstrated a significant second harmonic generation signal in the whole visible range. The developed materials and methods provide a platform for future infrared to visible converters based on silicon.

Harmonic signal generation and frequency upconversion at millimeter-wave bands are experimentally demonstrated by using selective sideband Brillouin amplification induced by stimulated Brillouin scattering in a single-mode fiber. The harmonic signals and frequency upconverted signals are simultaneously generated by the beating of optical sidebands, one of which is Brillouin amplified. By using this method, we successfully demonstrate generation of third-harmonic millimeter waves at 32.55 GHz with f(LO) of 10.85 GHz and upconversion of 10 Mbps quadrature-shift keyed data at f(IF) of 1.55 GHz into a 30 GHz band with more than 17 dB RF power gain.

Data-driven prediction of aerodynamic noise of transonic buffeting over an airfoil

Distributed acoustic sensing (DAS) is an ideal tool for ambient noise tomography owing to the dense spatial measurements and the ability to continuously record in harsh environments, such as underwater. Although the fine spatial sampling of DAS facilitates the imaging of small-scale lateral velocity heterogeneities, efforts relying on dispersion-based ambient noise tomography are hampered by the underlying premise of negligible lateral variations across the segment used for dispersion curve extraction. To image small-scale structures, this method should be augmented with objective and independent approaches that are not scale limited. Here, we show that power spectral densities (PSDs) and autocorrelations (ACs) of DAS data reveal extremely detailed frequency-dependent resonance and wave propagation characteristics. These observations contain crucial information on lateral and vertical wave propagation. We use these methods to demonstrate the ability to image a complex underwater basin using ambient noise recorded on a fiber deployed offshore Greece. A 2D shear-wave velocity model was derived by analyzing Scholte-wave dispersion. The PSD and AC reveal significant lateral variations across the short 2.5 km long fiber segment, including basin edge effects and scattered waves. These were used to further constrain and modify the velocity model. The modified model is supported by waveform simulations that qualitatively reproduce the PSD and AC observations. Our results demonstrate the advantages of incorporating PSD and AC observations into ambient noise-based imaging. The spatially continuous observation of resonance modes across the basin highlights the benefit of DAS acquisitions for ground-motion estimation.

We model the spectral signatures or spectral reflectance curves representing colors as power spectral density (PSD) functions, instead of considering them signals. Assuming that colors are generated by stationary random processes and deploying the Wiener-Khinchin theorem, we link the PSD of a color, thus the physical measurement of reflected or radiant energy, to the information provided by such spectrum. From the PSD, through the inverse Fourier transform, we recover the autocorrelation function of the corresponding random process. We propose ranking the spectral signatures of colors by imposing a lexicographic ordering of the autocorrelation function values. Such ranking can be deployed for the construction of nonlinear operators like morphological ones. We validate our approach on reference colors of a standard color set widely-used in colorimetry. We show the usefulness of our approach by computing morphological profiles for pixel classification using a widely-known hyperspectral image.

This paper outlines the most recent frequency and signal structure of COMPASS system. It then shows various power spectral density and autocorrelation function of B1, B2 and B3 signals, and summarizes the motivations in using BOC modulation after detailed analysis.