Amplitude-phase Method Research Articles

Investigating and Improving the Efficiency of Space-time Codes in Visible light Communication Systems based on a Multi-input-multi-output Channel Model

Background: Visible light communication (VLC) is a new communication method for transmitting information through semiconductor lighting devices. One of the applicable methods to improve the spectral efficiency of the system is the multi-input-multiple-output (MIMO) structure. Also, carrierless amplitude-phase (CAP) modulation is a high-dimensional modulation technique that can be used to improve the data transmission rate in modern communication systems. Methods: In this paper, carrierless amplitude-phase method is introduced in indoor optical communication systems to improve the performance of multi-input multi-output (MIMO) structures. The CAP modulation is considered a suitable method due to its low complexity and is introduced and studied in two structures with one carrier or CAP and multiple carriers or m-CAP. Results: In this study, the target system is simulated in m-CAP structures and the improvement is measured in the MIMO structure using this modulation. The results show that by using this method, the PAPR of the system was reduced compared to other research with the MIMO-OFDM structure. In addition, by not using FFT blocks, the computational and processing complexity was also reduced. Conclusion: It has been shown that the use of m-CAP increases the data transfer rate and improves the spectral efficiency of the system. In addition to CAP, spatial modulation schemes can also help improve the spectral efficiency and power efficiency of the system. Moreover, the space-time code is combined with m-CAP modulation and it is shown that this idea improves the efficiency of the MIMO system.

Low and intermediate energy cross section analysis of p-p and p-d elastic scattering using modified phase amplitude method for electromagnetic distorted nuclear interaction

The traditional phase function method is regarded as a resourceful tool for computing scattering phase shifts for quantum mechanical potential scattering involving local interactions. For the local plus a nonlocal potential the conventional phase function method does not hold good. In such a situation one has to modify it. The modified variable phase method is adapted here to treat the Manning-Rosen (MR) plus Graz nonlocal separable potential for constructing an exact expression for the phase function with rigorous inclusion of the electromagnetic effect. The merit of our analytical result is demonstrated by computing elastic scattering phase parameters and differential scattering cross sections for proton-proton (p − p) and proton-deuteron (p − d) systems which are in sensible agreement with previous works.

Acquisition of Spatial and Temporal Characteristics of Shallow Groundwater Movement Based on Long-Term Temperature Time Series in the Kangding Area, Eastern Tibetan Plateau

Heat has been widely used as a groundwater tracer to determine groundwater flow direction and velocity in a way that is ubiquitous, low-cost, environmentally friendly, and easy to use. However, temperature observations are generally short-term and small-scale, meaning they may not be able to reflect long-term changes in the characteristics of groundwater movement. In this study, we utilize 515 days of temperature data, collected from four measurement points in the Kangding area of the eastern Tibetan Plateau, in order to determine the spatial and temporal distribution of groundwater flow velocities using different analytical heat tracing methods. An analysis is conducted to evaluate the impact of thermal parameter uncertainties on the calculation of flow velocity, and a comparison is undertaken between the results of the phase, amplitude, and combined amplitude-phase methods. We subsequently discuss the relationship between flow velocity changes and precipitation. The results show that the estimated flow velocity is more susceptible to the volumetric heat capacity of the saturated sediment than it is to thermal conductivity. The phase method is more suitable for use in calculations in the study area, indicating that precipitation significantly impacts the flow velocity and that this impact is more pronounced in areas with flat terrain compared to areas with significant variation in elevation. Our research provides a comparative study of the heat tracing methods in areas with varied terrains and offers new evidence for the impact of precipitation and topography on groundwater infiltration.

A Technique for Multi-Parameter Signal Processing of an Eddy-Current Probe for Measuring the Thickness of Non-Conductive Coatings on Non-Magnetic Electrically Conductive Base Metals

The known amplitude-sensitive eddy-current method for measuring the thickness of non-conductive coatings on conductive non-magnetic base metals does not satisfy the accuracy requirements. A primary consideration is the significant influence of a change in the specific electrical conductivity of the base metals on results of measurements. In this study, we developed a technique for measuring the thickness of non-conductive coatings on non-magnetic conductive base metals by using the eddy-current amplitude-phase method and implemented algorithms to process obtained information. Our method considered the influence of the specific electrical conductivity of the base metals by forming a two-dimensional graduation characteristic of the thickness gauge by using several base metals with different specific electrical conductivity. The algorithm for point-in-polygon determination was applied, which allowed us to measure the thickness of the coatings and the specific electrical conductivity of the base metals as independent values. The equipment necessary to construct the two-dimensional graduation characteristic and the algorithm for calculation of the thickness are described in detail.

Possibilities of manual eddy current testing for measuring the depth of contact-fatigue cracks of the surface of rolling rails

The possibility of using the eddy current method to assess the depth of cracks in the surface of rolling rails in operation for planning the work of a rail grinding train is investigated. Experimental studies of the influence of the excitation frequency and the angle of inclination of the eddy current converter, the state of the surface, the depth and angle of inclination of the surface crack on the amplitude and phase of the eddy current signal are carried out. The possibilities of the amplitude-phase method of detuning from interfering factors associated with the slope of the transducer and the curvature of the controlled surface are determined. The resolution of the flaw detector was investigated when evaluating the characteristics of two or more closely spaced cracks - a defect of the "grid" type of cracks. The depth of surface cracks in the range from 0.1 to 1.4 mm was determined by metallographic examination after eddy current control. Optimal control parameters have been experimentally substantiated and a correlation between the crack depth and the projection of the signal amplitude in the direction perpendicular to the direction of change of the interfering factor - the angle of inclination of the transducer - has been established.

Construction of a reduced-order model of an electro-osmotic micromixer and discovery of attractors for petal structure

The chaotic state of microfluidic devices such as electroosmotic micromixers has received extensive attention. Its unsteady flow and multi-physics mask low-dimensional structure and potential attractors. Based on the dynamic mode decomposition and the sparse identification of nonlinear dynamics, this study aims to construct a manifold equation with the minimum degree of freedom, reveal the mixing mechanism of micromixers, and discover the evolution of chaotic states. The attenuation degree of freedom was introduced to force the modal coefficients to be pure oscillations. The six, four, and two-dimensional minimum reduced-order models (ROMs) were constructed under different mixing conditions. The nonlinear dynamics evolves on attractors resembling a six-petal structure based on the amplitude-phase method. The attractor periodicity and decay map the evolution of the periodic oscillation and limit cycle of the active modes and are related to the appearance of the low-energy dominant non-axisymmetric modes. These results emphasize the significance of ROM technology in revealing the low-dimensional structure and attractor of the electroosmotic micromixer.

Resonance method for measuring ionospheric plasma density onboard microsatellites

A method has been developed for diagnostics of the ionospheric plasma density on board a microsatellite using a resonator made on a segment of a two-wire line. The measurements of plasma parameters are based on the amplitude-phase method, which permits extanding the dynamic range of measured values by three orders of magnitude without increasing the resonator length. The paper presents a measurement technique and its experimental testing on a plasma setup under conditions as close as possible to the ionospheric ones. Keywords: micro- and nanosatellites, dielectric permittivity, resonance frequency, amplitude-phase method.

Резонансный метод измерения концентрации ионосферной плазмы на микроспутниках

A method has been developed for diagnostics of the ionospheric plasma density on board a microsatellite using a resonator made on a segment of a two-wire line. The measurements of plasma parameters are based on the amplitude-phase method, which permits extanding the dynamic range of measured values by three orders of magnitude without increasing the resonator length. The paper presents a measurement technique and its experimental testing on a plasma setup under conditions as close as possible to the ionospheric ones

On the Estimation of Resonance Widths of Field Line Resonances Using Ground Magnetometer Data

This paper presents a comparison of three methods to estimate the latitudinal resonance width of field line resonant, ultra-low frequency waves detected at the ground. These are a spatial domain, full-width half-maximum method and frequency domain amplitude-phase and amplitude-division methods. These methods were used to estimate the resonance width of several field line resonant intervals occurring on 26 November 2001, 1 October 2012, and 19 June 2015. The 19 June 2015 interval used data from one low, two mid, and one high latitudes. It was found that the resonance width estimates were different for each method and with how the data were processed. The most suitable methods and data processing were determined from a damped driven harmonic oscillator model. The amplitude-division methods yielded the most accurate results when the ground magnetic field data were processed with a boxcar window function or a frequency domain, exponential smoothing taper. The amplitude-phase method tended to underestimate the resonance width. The full-width half-maximum method gave accurate results for a high spatial resolution linear piece-wise curve fitted to the spectral amplitude with latitude profile. An accurate estimate of the latitudinal resonance width requires a correct choice of data processing, estimate method, resonance profile with latitude, and resonance model.

Comparison of maximum-likelihood mapping methods for gravitational-wave backgrounds

Detection of a stochastic background of gravitational waves is likely to occur in the next few years. Beyond searches for the isotropic component of SGWBs, there have been various mapping methods proposed to target anisotropic backgrounds. Some of these methods have been applied to data taken by the Laser Interferometer Gravitational-wave Observatories (LIGO) and Virgo. Specifically, these directional searches have focused on mapping the intensity of the signal on the sky via maximum likelihood solutions. We compare this intensity mapping approach to a previously proposed, but never employed, amplitude-phase mapping method to understand whether this latter approach may be employed in future searches. We build up our understanding of the differences between these two approaches by analysing simple toy models of time-stream data, and run mock-data mapping tests for the two methods. We find that the amplitude-phase method is only applicable to the case of a background which is phase-coherent on large scales or, at the very least, has an intrinsic coherence scale that is larger than that of the detector. Otherwise, the amplitude-phase mapping method leads to a loss of overall information, with respect to both phase and amplitude. Since we do not expect these phase-coherent properties to hold for any of the gravitational-wave background signals we hope to detect in the near future, we conclude that intensity mapping is the preferred method for such backgrounds.

Towards a Novel Super Current

For nonrelativistic two-electron atoms, we employ a phase-amplitude method to derive an energy-dependent three-body force which controls the dynamics of the atom near the threshold for double escape. Its potential energy has been taken into account to derive beyond a static adiabatic basis a novel partial differential equation that replaces an adiabatic basis. That equation whose solutions span a Banach space has been solved exactly in the energy window near threshold. In that energy range, we find the formation of unstable electron pairs, comparable to Cooper pairs. In contrast to Cooper pairs, our pairs are bound by dominant correlation rather than by the coupling to a phonon field. These ingredients are suspected to allow for a super current independent of the temperature.

Study of phase and amplitude-phase methods for measuring a reactive element quality factor

The paper considers improving accuracy of measured parameters and quality factors of reactive components. To increase the accuracy of measurement, circuit diagrams of new measuring transducers for measuring the quality factor of reactive elements for operation in a wide range of frequencies are developed. These measuring transducers provide reducing the standard uncertainty of the quality factor measurement for reactive elements with a slight complication of the measuring instrument. A phase and amplitude-phase methods of measuring the quality factor of reactive elements are considered, which provide the measurement standard uncertainty reduction. These methods have a relatively high measurement accuracy and are easy to implement on the microprocessor-based technology. Quality factors of inductive and capacitive elements are shown to be determined by measuring the phase shift angle between two output voltages of the measuring transducer. A prototype of the measuring transducer was installed to verify experimentally obtained theoretical results. Studies were performed for three inductors of different types and for low-power high-frequency capacitors. Theoretical and experimental dependences were investigated and compared.

Elastic statistical analysis of interval-valued time series

We investigate the problem of statistical analysis of interval-valued time series data – two nonintersecting real-valued functions, representing lower and upper limits, over a period of time. Specifically, we pay attention to the two concepts of phase (or horizontal) variability and amplitude (or vertical) variability, and propose a phase-amplitude separation method. We view interval-valued time series as elements of a function (Hilbert) space and impose a Riemannian structure on it. We separate phase and amplitude variability in observed interval functions using a metric-based alignment solution. The key idea is to map an interval to a point in , view interval-valued time series as parameterized curves in , and borrow ideas from elastic shape analysis of planar curves, including PCA, to perform registration, summarization, analysis, and modeling of multiple series. The proposed phase-amplitude separation provides a new way of PCA and modeling for interval-valued time series, and enables shape clustering of interval-valued time series. We apply this framework to three different applications, including finance, meteorology and physiology, proves the effectiveness of proposed methods, and discovers some underlying patterns in the data. Experimental results on simulated data show that our method applies to the point-valued time series.

Multivariate Analysis of Bivariate Phase-Amplitude Coupling in EEG Data Using Tensor Robust PCA.

Cross-frequency coupling is emerging as a crucial mechanism that coordinates the integration of spectrally and spatially distributed neuronal oscillations. Recently, phase-amplitude coupling, a form of cross-frequency coupling, where the phase of a slow oscillation modulates the amplitude of a fast oscillation, has gained attention. Existing phase-amplitude coupling measures are mostly confined to either coupling within a region or between pairs of brain regions. Given the availability of multi-channel electroencephalography recordings, a multivariate analysis of phase amplitude coupling is needed to accurately quantify the coupling across multiple frequencies and brain regions. In the present work, we propose a tensor based approach, i.e., higher order robust principal component analysis, to identify response-evoked phase-amplitude coupling across multiple frequency bands and brain regions. Our experiments on both simulated and electroencephalography data demonstrate that the proposed multivariate phase-amplitude coupling method can capture the spatial and spectral dynamics of phase-amplitude coupling more accurately compared to existing methods. Accordingly, we posit that the proposed higher order robust principal component analysis based approach filters out the background phase-amplitude coupling activity and predominantly captures the event-related phase-amplitude coupling dynamics to provide insight into the spatially distributed brain networks across different frequency bands.

Local Phase-Amplitude Joint Correction for Free Surface Velocity of Hopkinson Pressure Bar

The Hopkinson pressure bar is widely used to measure the reflected pressure of blast waves over a short distance. However, dispersion effects will occur when the elastic stress waves propagate in the pressure bar due to lateral inertia, and there will be errors between the signals obtained from the sensors and the actual loading. For the free surface velocity measured in our system, we developed a local phase-amplitude joint correction method to convert the measured velocity into the average reflected pressure of a shock wave at the impact end of the bar, considering factors such as propagation modes of the elastic wave, the frequency components’ time of arrival, velocity variation over the bar axis, and the stress–velocity relationship. Firstly, the Pochhammer–Chree frequency equation is calculated numerically, and the first to fourth orders of phase velocity, group velocity, normalized frequency, and propagation time curves of elastic wave propagation in 35CrMnSiA steel are obtained. Secondly, the phase and amplitude correction formulas for calculating average reflected pressure from center velocity are derived based on the propagation mode of the axial elastic wave in the pressure bar by analyzing the time-frequency combined spectrum obtained by short-time Fourier transform. Thirdly, a local phase-amplitude joint correction algorithm based on propagation mode is proposed in detail. The experimental tests and data analyses are carried out for eight sets of pressure bar. The results show that this method can identify the propagation mode of elastic waves in the bar intuitively and clearly. The first three orders of propagation modes are stimulated in the bar 04, while only the first order of propagation is stimulated in the other eight bars. The local phase-amplitude joint correction algorithm can avoid correcting the component of the non-axial elastic wave. The rising edge of the average stress curve on the impact surface of bar 01 and bar 04 is corrected from 4.13 μs and 4.09 μs to 2.70 μs, respectively.

Statistical Estimates of the Accuracy of Mono-Pulse Direction Finding of Sources of Radioemission by Dual-Channel Phase Devices

Formulation of the problem in general. The practice of radio monitoring indicates that information should be obtained on a time-to-real scale, with maximum speed and minimum time loss; the accuracy of the estimation of the parameters of the radioemission sources and their bearings should be maximized; the probability of recognizing and classifying sources and objects is no less than a given one. This confirms the existence of a problematic situation, which is caused by the existing contradiction between modern requirements for ensuring high speed, accuracy and reliability in the process of obtaining information, data and information and technical capabilities of modern radio monitoring facilities. Analysis of recent researches and publications. Currently, mono-pulse routing techniques are mainly designed to monitor radar signals where most of the signal parameters are known (example, carrier frequency, duration, period or frequency of pulse repetition, signal spectrum width, frequency deviation, signal to noise ratio). But in the conditions of partial or complete uncertainty of parameters, mono-pulse radar methods lose their efficiency and become unsuitable. Presenting the main material. The statistical estimates of the accuracy of the mono-pulse two-channel phasometric direction finding method, which provides unbiased, efficient and optimal estimates with a given probability and minimal mathematical expectation and variance, are calculated. The gain in the accuracy of direction finding when using two-phase phase direction finders will be determined by the ratio of the mean squared errors of the coarse and precise direction channels and equal to the inverse of the magnitudes of the phasometric bases of both channels. Conclusion. The use of mono-impulse dual-channel phase-finding method and defining the parameters of radioemission sources ensure unbiased, efficient and optimal estimates with a given probability and minimal mathematical expectation and variance. The minimization of the mathematical expectation and variance of the statistical estimates of the parameters of radio sources when using the two-channel phasometric method can be assured by rational choice of the magnitude of the phasometric bases of coarse and accurate channels and depends on the signal-to-noise ratio at the input of the direction finder and the accuracy of the carrier frequency measurement. The perspectives of future researches. One of the directions of further researches can be considered the solution of the problem of development of the combined amplitude-phase method (method) of bearing with synthesis of structural circuits of devices conducting mono-impulse bearing of sources of radio emission of telecommunication networks, which provide optimal estimation of relative radiation analysis evaluation of their quality indicators.

Phase-amplitude reduction far beyond the weakly perturbed paradigm.

While phase reduction is a well-established technique for the analysis of perturbed limit cycle oscillators, practical application requires perturbations to be sufficiently weak thereby limiting its utility in many situations. Here, a general strategy is developed for constructing a set of phase-amplitude reduced equations that is valid to arbitrary orders of accuracy in the amplitude coordinates. This reduction framework can be used to investigate the behavior of oscillatory dynamical systems far beyond the weakly perturbed paradigm. Additionally, a patchwork phase-amplitude reduction method is suggested that is useful when exceedingly large magnitude perturbations are considered. This patchwork method incorporates the high-accuracy phase-amplitude reductions of multiple nearby periodic orbits that result from modifications to nominal parameters. The proposed method of high-accuracy phase-amplitude reduction can be readily implemented numerically and examples are provided where reductions are computed up to fourteenth order accuracy.

Amplitude-phase method for solving Floquet-type problems

The understanding of one-dimensional quantal and dynamical problems is fundamental to problems involving stability of material constructions, quantum tunneling in solids, chemical selection of gas components, electronic properties of material nanostructures. An amplitude-phase method for one-dimensional Schrödinger/Hill-type equations with periodic potentials/coefficients is shown to provide detailed insights into Floquet-type quantal and dynamical problems. Method-independent real and periodic local amplitude and wave-number (or angular frequency) functions are found for bounded Floquet solutions. Regular and weakly singular periodic potentials/coefficients of analytic forms apply.

Discontinuous radial potentials, bound states and Dirac equations

Discontinuous, radial ‘square-well’ potentials of scalar and (time-component) vector types require special quantization conditions in Dirac equations transformed to second-order differential equations. Quantization conditions for positive energies are derived from first-order and second-order differential equations using amplitude-phase methods. Analytic condition for no orbital angular momentum of the large spinor component is obtained. Numerical applications relevant to independent-nucleon shell models illustrate level shifts due to shape (square-well/Woods–Saxon) differences.

Transition probability generating function of a transitionless quantum parametric oscillator.

The transitionless tracking (TT) algorithm enables the exact tracking of quantum adiabatic dynamics in an arbitrary short time by adding a counterdiabatic Hamiltonian to the original adiabatic Hamiltonian. By applying Husimi's method originally developed for a quantum parametric oscillator (QPO) to the transitionless QPO achieved using the TT algorithm, we obtain the transition probability generating function with a time-dependent parameter constituted with solutions of the corresponding classical parametric oscillator (CPO). By obtaining the explicit solutions of this CPO using the phase-amplitude method, we find that the time-dependent parameter can be reduced to the frequency ratio between the Hamiltonians without and with the counterdiabatic Hamiltonian, from which we can easily characterize the result achieved by the TT algorithm. We illustrate our theory by showing the trajectories of the CPO on the classical phase space, which elucidate the effect of the counterdiabatic Hamiltonian of the QPO.