Discrete Amplitude Research Articles

Discrete Mean Amplitude of Glycemic Excursion (MAGE) Measurement on Diabetics with Spline Interpolation Method

Discrete Mean Amplitude of Glycemic Excursion (MAGE) Measurement on Diabetics with Spline Interpolation Method

Modulation on Discrete Nonlinear Spectrum: Perturbation Sensitivity and Achievable Rates

Multi-soliton pulses are studied under small perturbations. By means of mutual information, we show that the nonlinear spectrum becomes correlated when a 64-PSK modulated 2-eigenvalues soliton is perturbed by a small additive white Gaussian noise (AWGN). Transmission over two channels are considered: an AWGN channel (back-to-back scenario) and an ideal optical fiber link with distributed noise. We numerically show that the Jost coefficients ${b}({\lambda }_{k})$ are less correlated than the discrete spectral amplitudes ${q}_{d}({\lambda }_{k})$ while either of them can be alternatively used for modulation. In both channels, we compare the achievable information rates (AIRs) of joint detection and separate detection if the modulation is over either ${q}_{d}({\lambda }_{k})$ or ${b}({\lambda }_{k})$ . We show that if the length of the link is relatively short, the separate detection of ${b}({\lambda }_{k})$ gives almost the same total information rate as the joint detection of ${b}({\lambda }_{k})$ or ${q}_{d}({\lambda }_{k})$ . Moreover, the AIRs are compared with one of a first-order soliton with the same modulation.

Extracting three-body breakup observables from continuum-discretized coupled-channels calculations with core excitations

Core-excitation effects in the scattering of two-body halo nuclei have been investigated in previous works. In particular, these effects have been found to affect in a significant way the breakup cross sections of neutron-halo nuclei with a deformed core. To account for these effects, appropriate extensions of the continuum-discretized coupled-channels (CDCC) method have been recently proposed. We aim to extend these studies to the case of breakup reactions measured under complete kinematics or semi-inclusive reactions in which only the angular or energy distribution of one of the outgoing fragments is measured. We use the standard CDCC method as well as its extended version with core excitations (XCDCC), assuming a pseudo-state basis for describing the projectile states. Two- and three-body observables are computed by projecting the discrete two-body breakup amplitudes, obtained within these reaction frameworks, onto two-body scattering states with definite relative momentum of the outgoing fragments and a definite state of the core nucleus. The presented method provides a tool to compute double and triple differential cross sections for outgoing fragments following the breakup of a two-body projectile, and might be useful to analyze breakup reactions with other deformed weakly-bound nuclei, for which core excitations are expected to play a role. We have found that, while dynamical core excitations are important for the proton target at intermediate energies, they are very small for the Zn target at energies around the Coulomb barrier.

Synthesis of Reconfigurable Antenna Array Using Differential Evolution Algorithm

ABSTRACTPresently certain applications demand two or more radiation patterns by using a single antenna array due to miniature and cost effective measures of the device. Hence, reconfigurable array is suitable for this purpose. This paper presents differential evolution (DE) algorithm based design of a reconfigurable antenna array. This method effectively obtains the optimum phase weights for efficient antenna performance in dual mode. The problem attempted is to find an optimal common amplitude weight distribution with minimum amplitude range ratio. 4-bit discrete amplitudes and 5-bit discrete phases have been considered to simplify the design of the array feed network. Based on simulation results, it is established that DE-based reconfigurable antenna array design provides better performance in terms of side lobe levels and null steering.

Approximation of Achievable Rates in Additive Gaussian Mixture Noise Channels

In this paper, we detail effective methods to approximate the achievable rates of channels with additive Gaussian mixture (GM) noise for both real and complex channels to achieve any desired level of accuracy. Attention is paid to a Gaussian input, a discrete real input, and a complex input with discrete amplitude and independent uniform phase. Such discrete inputs represent a wide range of input distributions and they include the capacity-achieving inputs as special cases. At first, we propose a simple technique to accurately calculate the noise entropy. Specifically, when the noise level is high, a lower bound on the integrand of the entropy is established and the noise entropy can be estimated using a closed-form solution. In the low noise region, the piecewise-linear curve fitting (PWLCF) method is applied. We then extend this result to calculate the achievable rate when the input is Gaussian distributed, which is shown to be asymptotically optimal. Next, we propose a simple PWLCF-based method to approximate the output entropy for a real GM channel when the input is discrete, and for a complex GM channel when the input is discrete in amplitude with independent uniform phase. In particular, for the real channel, the output entropy is evaluated by examining the output in high and low regions of amplitude using a lower bound on the integrand of the output entropy and PWLCF, respectively. For the complex channel, the output entropy is approximated a similar manner but using polar coordinates and the Kernel function. It is demonstrated that the output entropy, and consequently, the achievable rates, can be computed to achieve any given accuracy level.

Multieigenvalue Communication

In the most general case, all three components—the discrete eigenvalues, the discrete spectral amplitudes, and the continuous spectrum—of the nonlinear Fourier transform of a signal can be independently modulated. This paper examines information transmission using only the discrete eigenvalues, and presents heuristic designs for multisoliton signal sets with spectral efficiencies greater than 3 b/s/Hz. The first design, called multieigenvalue position encoding, is based on an exhaustive search followed by pruning of the signal set to remove high pulsewidth or high bandwidth outliers. The second design, called trellis encoding, achieves comparable efficiencies to the fist method at much lower complexity. These multisoliton signals do not undergo any pulse broadening, but are significantly limited by bandwidth expansion if the system length is not much smaller than the dispersion length parameter. This limitation suggests that modulating the eigenvalues alone cannot address the problem of nonlinearity in commercial fiber transmission systems, and that our proposed methods are only meaningful when dispersion is very small and dominated by nonlinearity, e.g., close to the zero-dispersion wavelength at 1300 nm.

Template-matching based detection of hyperbolas in ground-penetrating radargrams for buried utilities

Ground-penetrating radar (GPR) is a mature geophysical technique that is used to map utility pipelines buried within 1.5 m of the ground surface in the urban landscape. In this work, the template-matching algorithm has been originally applied to the detection and localization of pipe signatures in two perpendicular antenna polarizations. The processing of a GPR radargram is based on four main steps. The first step consists in defining a template, usually from finite-difference time-domain simulations, made of the nearby area of the hyperbola apex associated with the mean size object to be detected in the soil, whose mean permittivity has been previously experimentally estimated. In the second step, the raw radargram is pre-processed to correct variations due to antenna coupling, then the template matching algorithm is used to detect and localize individual hyperbola signatures in an environment containing unwanted reflections, noise and overlapping signatures. The distance between the shifted template and a local zone in the radargram, based on the L1 norm, allows us to obtain a map of distances. A user-defined threshold allows us to select a reduced number of zones having a high similarity measure. In the third step, minimum or maximum discrete amplitudes belonging to a selected hyperbola curve are semi-automatically extracted in each zone. In the fourth step, the discrete hyperbola data (i, j) are fitted by a parametric hyperbola model using a non-linear least squares criterion. The algorithm was implemented and evaluated on numerical radargrams, and afterwards on experimental radargrams.

Bi-Directional Algorithm for Computing Discrete Spectral Amplitudes in the NFT

The nonlinear Fourier transform represents a signal in terms of its continuous spectrum, discrete eigenvalues, and the corresponding discrete spectral amplitudes. This paper presents a new bi-directional algorithm for computing the discrete spectral amplitudes, which addresses the significant problem of rounding errors inherent in previously known techniques. We use the proposed method to obtain accurate spectral-domain noise statistics for 2-soliton signals using numerical simulation.

Single Photon Scattering Properties in Coupled-Resonator Waveguide Coupling with a Nanocavity Interacting with an External Mirror**Supported by the National Natural Science Foundation of China under Grant Nos. 11105001 and 61472282, the Anhui Provincial Natural Science Foundation under Grant Nos. 1408085QA22, 1608085MA09, and 1508085MF129.

We investigate theoretically single photon transport properties in coupled-resonator waveguide coupling with a nanocavity interacting with an external mirror. By using the discrete coordinates approach, transmission and reflection amplitudes of the propagating single photon in the waveguide are obtained. The influence of the coupling strength between the nanocavity and the external mirror on the single photon scattering spectra is discussed. We also extend the results to the waveguide with linear and quadratic form dispersion relations.

Adaptive Threshold Estimation for Variable Rate MQAM in Full-Duplex Systems With Imperfect CSI

The adaptive threshold estimation algorithm for discrete variable rate M-ary quadrature amplitude modulation (VR-MQAM) is investigated in full-duplex (FD) systems with imperfect channel state information (CSI). First, detailed FD system modeling is carried out, taking into account the differences from the half-duplex systems on rate adaptations. Then, in this model, we obtain the closed-form expression of the VR-MQAM spectral efficiency by deriving the distribution of the received signal to interference and noise ratio (SINR). Finally, we propose an adaptive threshold estimation scheme for VR-MQAM, which can adapt to the variation of imperfect CSI as well as residual self-interference (SI). Numerical results reveal that both residual SI and CSI imperfection depress the performance of VR-MQAM. Comparing to the existing variable threshold scheme, our adaptive scheme improves the spectral efficiency without any extra complexity.

The focused vectorial fields with ultra-long depth of focus generated by the tunable complex filter

According to the diffraction integral theory of vector field and the pupil filtering method with a discrete complex amplitude, we present a tunable pupil filter to achieve and manipulate the focused vector fields with ultra-long depth of focus. The filter consists of a polarization rotator with two /2 wave plates and a discrete complex amplitude filter with six zones. Amplitude transmissions of these zones are different and increase along the radial direction. And every two adjacent transmitted zones have the opposed phases 0 and . With optimized cylindrical polarization (0 =52) and discrete amplitude, the generalized cylindrical vector field can be tightly focused into a three-dimensional (3D) flat-top field with an extended depth of focus (～10 ) by a high numerical aperture lens. For the main outermost zone and the other five inner zones, we analyze the intensity distributions of the three polarized components and the total polarized component in the focal region. We find that the axially and azimuthally polarized components are the major contributors. The outermost zone offers the central field of the focused field while the other five zones affect the side lobe more obviously. Through adjusting the included angle between the double wave plates, we can change the polarization states of the incident vector field and alter the structures of the focused fields among the 3D flat-top focused field, needle-like field, tube-like field and the other fields with intermediate form. Result obtained is superior to that of the past research for the adjustable freedom between these forms, and it reveals the dynamic relation between the evolved vectorial form of incident field and the vector structure of the focused field. Our work paves a way to achieve the controlled dynamical focused field with a long depth of focus. The needle-like field, tube-like field and the well-matched 3D flat-top focused field will meet the demand of applications in optical microscope, optical micro-manipulating, optical micromachining and so on.

Instantaneous Frequency Estimation of Multi-Component Non- Stationary Signals using Fourier Bessel series and Time-Varying Auto Regressive Model

Abstract In this paper, we propose a novel technique for Instantaneous Frequency (IF) estimation of multi component non stationary signals using Fourier Bessel Series and Time- Varying Auto Regressive (FB-TVAR) model. In the proposed technique, the Fourier-Bessel (FB) expansion decomposes the multi-component non stationary signal into a number of monocomponent signals and TVAR model is used to model each mono-component signal. In TVAR modeling approach the time varying parameters are expanded as a linear combination of basis functions. In this paper, the TVAR parameters are expanded by a discrete cosine basis functions. The maximum likelihood estimation algorithm for model order selection in TVAR models is also discussed. The Instantaneous Frequency (IF) is extracted from the time-varying parameters by calculating the angles of the estimation error filter polynomial roots. The estimation of the TVAR parameters of a multicomponent signal requires the inversion of a large covariance matrix, while the projected technique (FB-TVAR) requires the inversion of a number of comparatively small covariance matrices with better numerical stability properties. Simulation results are presented for Multi component discrete Amplitude and Frequency modulated (AM-FM) signal

Capacity-Achieving Input Distributions of Additive Quadrature Gaussian Mixture Noise Channels

This paper studies the characterization of the optimal input and the computation of the capacity of additive quadrature Gaussian mixture (GM) noise channels under an average power constraint. The considered model can be used to represent a wide variety of channels with impulsive interference, such as the well-known Bernoulli-Gaussian and Middleton class-A impulsive noise channels, as well as multiple-access interference channels and cognitive radio channels under imperfect sensing. At first, we demonstrate that there exists a unique input distribution that achieves the channel capacity, and the capacity-achieving input distribution has a uniformly distributed phase. By examining the Kuhn-Tucker alignment conditions (KTCs), we further show that, if the optimal input amplitude distribution contains an infinite number of mass points on a bounded interval, the channel output must be Gaussian-distributed. However, by using Bernstein's theorem to examine the completely monotonic condition, it is shown that the assumption of a Gaussian-distributed output is not valid. As a result, there are always a finite number of mass points on any bounded interval in the optimal amplitude distribution. In addition, by applying a novel bounding technique on the KTC and using the envelop theorem, we demonstrate that the optimal amplitude distribution cannot have an infinite number of mass points. This gives us the unique solution of the optimal input having discrete amplitude with a finite number of mass points. Given this discrete nature of the optimal input, we then develop a simple method to compute the discrete optimal input and the corresponding capacity. Our numerical examples show that, in many cases, the capacity-achieving distribution consists of only one or two mass points.

SYNTHESIS OF DUAL RADIATION PATTERN OF RECTANGULAR PLANAR ARRAY ANTENNA USING EVOLUTIONARY ALGORITHM

A pattern synthesis method based on Evolutionary Algorithm is presented to generate a dual radiation pattern from a planar array of isotropic antennas. The desired patterns are obtained by finding out optimum set of elements excitations. Flat-top and Pencil beams share a common optimum amplitude distribution among the array elements. Flat-top beam is generated by updating the zero phases with the optimum phases among the elements. 4 bit discrete amplitudes and 5 bit discrete phases have been taken to simplify the design of the feed network. Results clearly show the effectiveness of the proposed method.

DFT-based optical offset-QAM OFDM: analytical, numerical, and experimental studies

We investigate discrete Fourier transform-based offset quadrature amplitude modulation (offset-QAM) orthogonal frequency division multiplexing (OFDM) technology. We derive a closed-form expression for the de-multiplexed signal and analyze the influence of crosstalk on implementation algorithms and system performance. It is found that channel estimation in offset-QAM OFDM is different from that in conventional OFDM (C-OFDM) due to the residual crosstalk terms and requires particular study. We propose simple and efficient channel estimation algorithms and show, in a 38-Gbit/s offset-16QAM OFDM experiment with 840-km single-mode fiber, that these algorithms can enable the system performance close to the theoretical limit. By using these algorithms, we compare this technology with C-OFDM and Nyquist FDM (N-FDM) and numerically and experimentally show that DFT-based offset-QAM OFDM can greatly enhance the net data rate for fiber transmissions compared to C-OFDM and exhibit lower complexity than N-FDM. These advantages together with the successfully developed implementation algorithms make this technology very promising for optical communication systems.

Graph-cut based discrete-valued image reconstruction.

Efficient graph-cut methods have been used with great success for labeling and denoising problems occurring in computer vision. Unfortunately, the presence of linear image mappings has prevented the use of these techniques in most discrete-amplitude image reconstruction problems. In this paper, we develop a graph-cut based framework for the direct solution of discrete amplitude linear image reconstruction problems cast as regularized energy function minimizations. We first analyze the structure of discrete linear inverse problem cost functions to show that the obstacle to the application of graph-cut methods to their solution is the variable mixing caused by the presence of the linear sensing operator. We then propose to use a surrogate energy functional that overcomes the challenges imposed by the sensing operator yet can be utilized efficiently in existing graph-cut frameworks. We use this surrogate energy functional to devise a monotonic iterative algorithm for the solution of discrete valued inverse problems. We first provide experiments using local convolutional operators and show the robustness of the proposed technique to noise and stability to changes in regularization parameter. Then we focus on nonlocal, tomographic examples where we consider limited-angle data problems. We compare our technique with state-of-the-art discrete and continuous image reconstruction techniques. Experiments show that the proposed method outperforms state-of-the-art techniques in challenging scenarios involving discrete valued unknowns.

Utilizing spectral decomposition to determine the distribution of injected CO2 at the Snøhvit Field

ABSTRACTTime‐lapse 3D seismic reflection data, covering the CO2 storage operation at the Snøhvit gas field in the Barents Sea, show clear amplitude and time‐delay differences following injection. The nature and extent of these changes suggest that increased pore fluid pressure contributes to the observed seismic response, in addition to a saturation effect.Spectral decomposition using the smoothed pseudo‐Wigner–Ville distribution has been used to derive discrete‐frequency reflection amplitudes from around the base of the CO2 storage reservoir. These are utilized to determine the lateral variation in peak tuning frequency across the seismic anomaly as this provides a direct proxy for the thickness of the causative feature.Under the assumption that the lateral and vertical extents of the respective saturation and pressure changes following CO2 injection will be significantly different, discrete spectral amplitudes are used to distinguish between the two effects. A clear spatial separation is observed in the distribution of low‐ and high‐frequency tuning. This is used to discriminate between direct fluid substitution of CO2, as a thin layer, and pressure changes that are distributed across a greater thickness of the storage reservoir. The results reveal a striking correlation with findings derived from pressure and saturation discrimination algorithms based on amplitude versus offset analysis.

Long-term history and immediate preceding state affect EEG slow wave characteristics at NREM sleep onset in C57BL/6 mice.

The dynamics of cortical activity across the 24-h day and at vigilance state transitions is regulated by an interaction between global subcortical neuromodulatory influences and local shifts in network synchrony and excitability. To address the role of long-term and immediate preceding history in local and global cortical dynamics, we investigated cortical EEG recorded from both frontal and occipital regions during an undisturbed 24-h recording in mice. As expected, at the beginning of the light period, under physiologically increased sleep pressure, EEG slow waves were more frequent and had higher amplitude and slopes, compared to the rest of the light period. Within discrete NREM sleep episodes, the incidence, amplitude and slopes of individual slow waves increased progressively after episode onset in both derivations by approximately 10-30%. Interestingly, at the beginning of NREM sleep episodes slow waves in the frontal and occipital derivations frequently occurred in isolation, as quantified by longer latencies between consecutive slow waves in the two regions. Notably, slow waves during the initial period of NREM sleep following REM sleep episodes were significantly less frequent, lower in amplitude and exhibited shallower slopes, compared to those that occurred in NREM episodes after prolonged waking. Moreover, the latencies between consecutive frontal and occipital NREM slow waves were substantially longer when they occurred directly after REM sleep compared to following consolidated wakefulness. Overall these data reveal a complex picture, where both time of day and preceding state contribute to the characteristics and dynamics of slow waves within NREM sleep. These findings suggest that NREM sleep initiates in a more "local" fashion when it occurs following REM sleep episodes as opposed to sustained waking bouts. While the mechanisms and functional significance of such a re-setting of brain state after individual REM sleep episodes remains to be investigated, we suggest that it may be an essential feature of physiological sleep regulation.

Long-term history and immediate preceding state affect EEG slow wave characteristics at NREM sleep onset in C57BL/6 mice

The dynamics of cortical activity across the 24-h day and at vigilance state transitions is regulated by an interac- tion between global subcortical neuromodulatory influences and local shifts in network synchrony and excitability. To address the role of long-term and immediate preceding history in local and global cortical dynamics, we inves- tigated cortical EEG recorded from both frontal and occipital regions during an undisturbed 24-h recording in mice. As expected, at the beginning of the light period, under physiologically increased sleep pressure, EEG slow waves were more frequent and had higher amplitude and slopes, compared to the rest of the light period. Within discrete NREM sleep episodes, the incidence, amplitude and slopes of individual slow waves increased progres- sively after episode onset in both derivations by approximately 10-30%. Interestingly, at the beginning of NREM sleep episodes slow waves in the frontal and occipital derivations frequently occurred in isolation, as quantified by longer latencies between consecutive slow waves in the two regions. Notably, slow waves during the initial period of NREM sleep following REM sleep episodes were significantly less frequent, lower in amplitude and exhibited shallower slopes, compared to those that occurred in NREM episodes after prolonged waking. Moreover, the laten- cies between consecutive frontal and occipital NREM slow waves were substantially longer when they occurred directly after REM sleep compared to following consolidated wakefulness. Overall these data reveal a complex picture, where both time of day and preceding state contribute to the characteristics and dynamics of slow waves within NREM sleep. These findings suggest that NREM sleep initiates in a more “local” fashion when it occurs following REM sleep episodes as opposed to sustained waking bouts. While the mechanisms and functional signifi- cance of such a re-setting of brain state after individual REM sleep episodes remains to be investigated, we suggest that it may be an essential feature of physiological sleep regulation.

Long-term history and immediate preceding state affect EEG slow wave characteristics at NREM sleep onset in C57BL/6 mice

The dynamics of cortical activity across the 24-h day and at vigilance state transitions is regulated by an interac- tion between global subcortical neuromodulatory influences and local shifts in network synchrony and excitability. To address the role of long-term and immediate preceding history in local and global cortical dynamics, we inves- tigated cortical EEG recorded from both frontal and occipital regions during an undisturbed 24-h recording in mice. As expected, at the beginning of the light period, under physiologically increased sleep pressure, EEG slow waves were more frequent and had higher amplitude and slopes, compared to the rest of the light period. Within discrete NREM sleep episodes, the incidence, amplitude and slopes of individual slow waves increased progres- sively after episode onset in both derivations by approximately 10-30%. Interestingly, at the beginning of NREM sleep episodes slow waves in the frontal and occipital derivations frequently occurred in isolation, as quantified by longer latencies between consecutive slow waves in the two regions. Notably, slow waves during the initial period of NREM sleep following REM sleep episodes were significantly less frequent, lower in amplitude and exhibited shallower slopes, compared to those that occurred in NREM episodes after prolonged waking. Moreover, the laten- cies between consecutive frontal and occipital NREM slow waves were substantially longer when they occurred directly after REM sleep compared to following consolidated wakefulness. Overall these data reveal a complex picture, where both time of day and preceding state contribute to the characteristics and dynamics of slow waves within NREM sleep. These findings suggest that NREM sleep initiates in a more “local” fashion when it occurs following REM sleep episodes as opposed to sustained waking bouts. While the mechanisms and functional signifi- cance of such a re-setting of brain state after individual REM sleep episodes remains to be investigated, we suggest that it may be an essential feature of physiological sleep regulation.