Nonlinear Frequency Domain Research Articles

Modelling the Asymmetric Impact of Terrorism and Military Expenditure on Tourism Development

This study evaluates the asymmetric effects of terrorist attacks and military spending on India's tourism sector by considering gross capital formation and foreign direct investment inflows in the tourism function as controlled variables. Considering the period 1980 to 2017, we employed a non-linear autoregressive distributed lag (NARDL) model and frequency domain causality. This study found that a 1% positive (negative) shock in the partial sum of the terrorist incidents would decrease (increase) the tourist arrivals by 0.17% (0.19%), respectively. However, a positive shock in the partial sum of military spending would enhance tourist arrivals, while a negative shock would lower them both in the short and long run. In addition, gross capital formation and foreign direct investment inflows favourably influence India's tourism development in the long run. The findings from frequency domain casualty also resonate with this study's short-run and long-run findings.

Nonlinear frequency domain spline prioritization optimization generalized maximum correntropy criterion evolved momentum adaptive filtering

Nonlinear frequency domain spline prioritization optimization generalized maximum correntropy criterion evolved momentum adaptive filtering

P300 intention recognition based on phase lag index (PLI)-rich-club brain functional network.

Brain-computer interface (BCI) technology based on P300 signals has a broad application prospect in the assessment and diagnosis of clinical diseases and game control. The paper of selecting key electrodes to realize a wearable intention recognition system has become a hotspot for scholars at home and abroad. In this paper, based on the rich-club phenomenon that exists in the process of intention generation, a phase lag index (PLI)-rich-club-based intention recognition method for P300 is proposed. The rich-club structure is a network consisting of electrodes that are highly connected with other electrodes in the process of P300 generation. To construct the rich-club network, this paper uses PLI to construct the brain functional network, calculates rich-club coefficients of the network in the range of k degrees, initially identifies rich-club nodes based on the feature of node degree, and then performs a descending order of betweenness centrality and identifies the nodes with larger betweenness centrality as the specific rich-club nodes, extracts the non-linear features and frequency domain features of Rich-club nodes, and finally uses support vector machine for classification. The experimental results show that the range of rich-club coefficients is smaller with intent compared to that without intent. Validation was performed on the BCI Competition III dataset by reducing the number of channels to 17 and 16 for subject A and subject B, with recognition quasi-departure rates of 96.93% and 94.93%, respectively, and on the BCI Competition II dataset by reducing the number of channels to 17 for subjects, with a recognition accuracy of 95.50%.

Joint equalization of frequency offset and phase noise using two-stage cascaded extended Kalman filter for discrete spectrum 16/64APSK NFDM systems.

For the discrete spectrum nonlinear frequency division multiplexing (DS-NFDM) 16/64 amplitude phase shift keying (APSK) system, the inevitable laser impairments including frequency offset (FO) and carrier phase noise (CPN) would cause different rotations of the received signal constellations. In addition, the combined effect of FO and amplifier spontaneous emission (ASE) noise induces the eigenvalue shift, accordingly the residual channel impairment (RCI) is inevitably yielded. To address the above problems, we deduce the joint impairment model of FO, CPN and RCI, and then propose a joint equalization scheme using two-stage cascaded extended Kalman filter (TSC-EKF) for these impairments. It performs frequency offset compensation in the first stage, subsequently carries out joint equalization of CPN and RCI in the second stage. Meanwhile, the minimum Euclidean distance and phase difference between the received symbols and the ideal 16/64APSK constellations are ingeniously fused to calculate the innovations of TSC-EKF. The effectiveness has been verified by 2 GBaud DS-NFDM 16/64 APSK simulations and DS-NFDM 16APSK transmission experiments. The results demonstrate that when performing the joint equalization of FO, CPN and RCI, the maximum FOE range of TSC-EKF scheme achieves 1.2 and 9.6 times as that of nonlinear frequency domain (NFD) scheme and fast Fourier transform -Like (FFT-Like) scheme, respectively. Furthermore, its maximum LW tolerance reaches 3.3 times as that of the M-th power scheme. Importantly, the complexity of TSC-EKF is 63.4% as that of NFD scheme and on an order of O(N).

An eigenvalue-shift and matching-signal based FOE method for discrete spectrum modulated NFDM system

We propose an improved frequency offset estimation (FOE) algorithm based on eigenvalue-shift and matching-signal (ESMS) for discrete spectrum modulated nonlinear frequency division multiplexing (NFDM) system, which can realize high estimation accuracy without the constraint of the Baud-rate. Meanwhile, its computational complexity is lower in contrast with nonlinear frequency domain (NFD) method. Therefore, the proposed method is more powerful for eigenvalue NFDM transmission systems with large FO variation.

Numerical analysis of the performance of a composite marine propeller blade subject to structural blade oscillations

High-fidelity Large Eddy Simulations (LES) are conducted over the oscillating marine propeller blades to investigate the effects of blade oscillation on the unsteady flow behaviour as well as to analyse the performance of the composite marine propeller blades. The accuracy of the results is first verified against the reference experimental results. A nonlinear frequency-domain solution or harmonic solution method is also applied to this study, based on a high-fidelity LES model, in addition to the traditional time-domain solution method to investigate the capabilities of the frequency-domain method in predicting the unsteady flow parameters, vortex generation, and hydrodynamic damping to determine the stability of the propeller blades. Results obtained reveal that the oscillation of the blade has a great impact on the vortex generation process which could impose implications on the performance and structural integrity of the composite marine propeller blades.

A prince for the sleeping beauty - NFT for soliton signal processing

The soliton, the eigen-solution of nonlinear Schrodinger equation (NLSE), has been investigated in many branches of physics. The first prediction of a soliton in optical fiber could be dated back to 1973. Since then, numerous theoretical and experimental works on solitons have been carried out, including soliton communication and soliton generation in fiber lasers. However, due to the constraints of hardware and digital signal processing methods, research on solitons have been stalled for decades. Recently, the nonlinear Fourier transform (NFT) has attracted significant attention in the field of optical fiber communications and soliton-based signal processing, which provides a powerful mathematical framework for analyzing and understanding the behavior of solitons in optical fibers, enabling the development of novel signal processing techniques. The NFT technique has brought the soliton back to life. It has been widely recognized that in nonlinear frequency domain, the nonlinear crosstalk resulting from the Kerr effect is practically negligible, and fiber nonlinearity damage caused by the Kerr effect can be accounted for as a linear transform factor. Moreover, NFT has been demonstrated for the analysis of laser radiation, highlighting its potential in characterizing ultrafast pulses in the nonlinear frequency domain. In this submission, we review the advancements of NFT concerning both in soliton communication and characterization, focusing on practical implementation aspects. With many practical implementation aspects still being open, our mini review is aimed to assist researchers in evaluating the potential, identifying challenges, and envisioning future directions in NFT-based signal processing technologies. And wake up the sleeping beauty – the soliton!

Depression Detection Based on Analysis of EEG Signals in Multi Brain Regions.

As an objective method to detect the neural electrical activity of the brain, electroencephalography (EEG) has been successfully applied to detect major depressive disorder (MDD). However, the performance of the detection algorithm is directly affected by the selection of EEG channels and brain regions. To solve the aforementioned problems, nonlinear feature Lempel-Ziv complexity (LZC) and frequency domain feature power spectral density (PSD) were extracted to analyze the EEG signals. Additionally, effects of different brain regions and region combinations on detecting MDD were studied with eyes closed and opened in a resting state. The mean LZC of patients with MDD was higher than that of the control group, and the mean PSD of patients with MDD was generally lower than that of the control group. The temporal region is the best brain region for MDD detection with a detection accuracy of 87.4%. The best multi brain regions combination had a detection accuracy of 92.4% and was made up of the frontal, temporal, and central brain regions. This paper validates the effectiveness of multiple brain regions in detecting MDD. It provides new ideas for exploring the pathology of MDD and innovative methods of diagnosis and treatment.

Machine Learning Enabled P300 Classifier for Autism Spectrum Disorder Using Adaptive Signal Decomposition

Joint attention skills deficiency in Autism spectrum disorder (ASD) hinders individuals from communicating effectively. The P300 Electroencephalogram (EEG) signal-based brain-computer interface (BCI) helps these individuals in neurorehabilitation training to overcome this deficiency. The detection of the P300 signal is more challenging in ASD as it is noisy, has less amplitude, and has a higher latency than in other individuals. This paper presents a novel application of the variational mode decomposition (VMD) technique in a BCI system involving ASD subjects for P300 signal identification. The EEG signal is decomposed into five modes using VMD. Thirty linear and non-linear time and frequency domain features are extracted for each mode. Synthetic minority oversampling technique data augmentation is performed to overcome the class imbalance problem in the chosen dataset. Then, a comparative analysis of three popular machine learning classifiers is performed for this application. VMD's fifth mode with a support vector machine (fine Gaussian kernel) classifier gave the best performance parameters, namely accuracy, F1-score, and the area under the curve, as 91.12%, 91.18%, and 96.6%, respectively. These results are better when compared to other state-of-the-art methods.

Exploring the asymmetric effect of COVID-19 pandemic news on the cryptocurrency market: evidence from nonlinear autoregressive distributed lag approach and frequency domain causality

This paper explores the asymmetric effect of COVID-19 pandemic news, as measured by the coronavirus indices (Panic, Hype, Fake News, Sentiment, Infodemic, and Media Coverage), on the cryptocurrency market. Using daily data from January 2020 to September 2021 and the exponential generalized autoregressive conditional heteroskedasticity model, the results revealed that both adverse and optimistic news had the same effect on Bitcoin returns, indicating fear of missing out behavior does not prevail. Furthermore, when the nonlinear autoregressive distributed lag model is estimated, both positive and negative shocks in pandemic indices promote Bitcoin’s daily changes; thus, Bitcoin is resistant to the SARS-CoV-2 pandemic crisis and may serve as a hedge during market turmoil. The analysis of frequency domain causality supports a unidirectional causality running from the Coronavirus Fake News Index and Sentiment Index to Bitcoin returns, whereas daily fluctuations in the Bitcoin price Granger affect the Coronavirus Panic Index and the Hype Index. These findings may have significant policy implications for investors and governments because they highlight the importance of news during turbulent times. The empirical results indicate that pandemic news could significantly influence Bitcoin’s price.

The relationship between geopolitical risk and crude oil prices: evidence from nonlinear and frequency domain causality tests

ABSTRACT This paper aims to investigate the possible explanatory effect of geopolitical risks on the oil price changes from February 1986 to December 2019 by employing the nonlinear bivariate Granger causality test and frequency domain Granger causality test based on the geopolitical risk index. The results suggest that there exists a nonlinear causality from geopolitical risks to crude oil prices. Moreover, geopolitical risks have a short-term impact on oil prices, less than 12 months. Actual geopolitical events have a smaller and less lasting impact on oil prices than pure geopolitical risks.

Asymmetric effect of political stability on production-based CO2 emissions in the UK: long-run evidence from nonlinear ARDL and frequency domain causality.

The study deals with the effect of political stability on environmental degradation in the long run for the United Kingdom (UK). For this aim, the political stability effect on production-based carbon dioxide (CO2) emissions is examined by considering trade openness, renewable energy, and economic growth and using quarterly data between 1995/Q1 and 2018/Q4. Nonlinear autoregressive distributed lag (NARDL), which allows the researcher to measure the asymmetric impact of explanatory indicators positively or negatively, is performed as the empirical approach. Also, Breitung & Candelon (BC) frequency domain causality test is applied to measure the causality effect of explanatory variables on CO2 emissions. The results reveal that (i) political stability has a statistically significant effect on production-based CO2 emissions and positive shocks have a higher power than negative shocks; (ii) economic growth has an increasing effect, whereas renewable energy has a decreasing effect on production-based CO2 emissions; and (iii) there is frequency domain causality from political risk, economic growth, renewable energy consumption, and trade openness to production-based CO2 emissions. Hence, empirical results highlight the asymmetric effect of political stability on environmental degradation in the long run for UK. Thus, UK policymakers should consider political stability in policy development and implementation process for limiting CO2 emissions in the long run.

Nonlinear wave energy dissipator with wave attenuation and energy harvesting at low frequencies

It is important to determine how to reduce the wave load and utilize the ocean energy through the hybrid wave attenuation and energy harvesting structure (WAAEHS) as it is the basic scientific problem in the field of ocean engineering. The existing linear hybrid devices have poor performance due to the mismatch between the natural frequency and the excitation frequency in the low frequency region. The method of increasing the mass is unreliable and low economic, and the introduction of nonlinear mechanism to reduce the stiffness has complex fluid-structure coupling problem between waves and structures. In this paper, a new type of negative stiffness mechanism with a simple structure and good stability has been proposed and applied to a hybrid WAAEHS, and a nonlinear frequency domain method combining eigenfunction expansion matching method(EEMM)and multi-harmonic balance method(MHBM) has been proposed to solve the nonlinear wave–structure interaction dynamic model. The influence of the key parameters of the mechanism on the wave attenuation and energy harvesting performance is examined, and the “phase control” mechanism of the negative stiffness mechanism is revealed to improve the low-frequency wave attenuation and energy harvesting performance.

An Estimated δ-Based Iterative Block Decision Feedback Equalization in SC-FDE System

We provide a novel nonlinear frequency domain equalization algorithm for the frequency domain equalization of an SC-FDE system by improving the classical iterative block decision feedback equalization (IBDFE) algorithm and applying δ estimation to the improved algorithm. The improvement of the IBDFE algorithm is carried out by replacing the ZF equalization in the feedback branch with the MMSE equalization and eliminating the iteration of the correlation factor, thus reducing the noise error and the computational complexity of the original algorithm. δ estimation can estimate residual inter-symbol interference in the signal after MMSE equalization and reject it, thus further improving the equalization accuracy. The simulation results show that the performance of the novel algorithm is better than that of the IBDFE algorithm with similar complexity, or the complexity of the novel algorithm is lower than that of the IBDFE algorithm with similar performance.

10.83 Tb/s Over 800 Km Nonlinear Frequency Division Multiplexing WDM Transmission

Nonlinear frequency division multiplexing (NFDM) transmission scheme has attracted great interest in optical fiber communication systems due to its potential for surpassing the Kerr nonlinearity limit. There have been very active studies on single-channel NFDM transmission systems recently. However, up to now, few experiments have validated the feasibility of applying NFDM into wavelength division multiplexing (WDM) optical communication systems toward high-capacity transmission for wideband coverage. Moreover, the overall performance of the NFDM system is restricted due to many challenges in theoretical design and practical implementation. Novel neural network-based equalization methods contribute to eliminating multi-dimensional crosstalk, hence prompting the NFDM system performance. In this article, we experimentally demonstrate a high-capacity NFDM-WDM transmission system enabled by the newly developed digital signal processing (DSP) algorithms. With data modulation on the continuous spectrum in nonlinear frequency domain, a 25-channel WDM system with polarization division multiplexing (PDM) 16-ary quadrature amplitude modulation (16-QAM) transmitting over 800 km standard single-mode fiber (SSMF) is successfully achieved. To mitigate the undesirable correlations between the nonlinear continuous spectral components, a nonlinear spectrum equalization scheme based on artificial neural network (ANN) is utilized in the receiver side DSP. Through this ANN-based spectrum equalization, a 0.63 dB Q <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -factor gain is achieved compared to the conventional equalization scheme. A record transmission capacity of 10.83 Tb/s is achieved in a 25-channel WDM system over 800 km SSMF, with a remarkable single-channel line rate of 433.3 Gb/s. Our work reports the highest capacity NFDM-WDM transmission up to date and helps to further explore the inherent ability of NFDM to resist fiber channel nonlinearity.

Low-frequency energy capture and water wave attenuation of a hybrid WEC-breakwater with nonlinear stiffness

Wave energy is attractive for its generous, sustainable and clean, the combination of floating breakwater (FB) and wave energy converter (WEC) is an economical approach to capture wave energy and attenuate waves. The conventional hybrid WEC-FB system is ineffective for low-frequency waves. To overcome this shortcoming, this paper proposed a novel WEC-FB with nonlinear stiffness mechanism to improve its wave attenuation and power capture performance. A hybrid semi-analytical nonlinear frequency-domain approach including the eigenfunction expansion matching method (EEMM) and multi-harmonic balance method (MHBM) is proposed to solve the nonlinear waves-structures interaction problem. The performance of the nonlinear WEC-FB is demonstrated by comparing with conventional linear counterpart, and the underlying reason for the effect of nonlinear mechanism is explored. The phase control mechanism for improving low frequency performance of wave elimination and energy capture is revealed by using the analytical method. This study shows that the introduction of the nonlinear mechanism can both improve the wave attenuation and energy absorption performance, especially in the low-frequency wave region.

The nexus of disaggregated energy sources and cement production carbon emission in China

Cement production reportedly accounts for the largest global materials flow, thus achieving global environmental sustainability through responsible consumption and production is central to the sustainable development scenario. But even that China, the world's largest carbon emitter and largest cement producer, is under-studied. Thus, the current study employed the nonlinear ARDL and frequency domain causality methods to unearth the contributory or mitigating role of energy sources and economic progress in China's cement carbon emission (CCE) over the period 1971-2020. Overall, the study establishes long-run equilibrium relationship between the study variables of interest Subsequently, the baseline regression suggests that a positive shift in economic growth, energy from fossil fuel and primary energy consumption all increase emissions while a negative shift does not have a significant effect on emissions. Moreover, a positive (negative) shift in renewable energy decreases (increases) emissions in both the short and long-run. The result of the Frequency Domain causality analysis resonates with the results of NARDL regression. As a policy, this study infers energy development and economic-related measures are strategically important in achieving sustainable cement production and consumption.

Signal Quality Improvement in Downlink Power Domain NOMA with Blind Nonlinear Compensator and Frequency Domain Equalizer

Signal Quality Improvement in Downlink Power Domain NOMA with Blind Nonlinear Compensator and Frequency Domain Equalizer

Nonlinear Fourier transform assisted high-order soliton characterization

Nonlinear Fourier transform (NFT), based on the nonlinear Schrödinger equation, is implemented for the description of soliton propagation, and in particular focused on propagation of high-order solitons. In nonlinear frequency domain, a high-order soliton has multiple eigenvalues depending on the soliton amplitude and pulse-width. During the propagation along the standard single mode fiber (SSMF), their eigenvalues remain constant, while the corresponding discrete spectrum rotates along with the SSMF transmission. Consequently, we can distinguish the soliton order based on its eigenvalues. Meanwhile, the discrete spectrum rotation period is consistent with the temporal evolution period of the high-order solitons. The discrete spectrum contains nearly 99.99% energy of a soliton pulse. After inverse-NFT on discrete spectrum, soliton pulse can be reconstructed, illustrating that the eigenvalues can be used to characterize soliton pulse with good accuracy. This work shows that soliton characteristics can be well described in the nonlinear frequency domain. Moreover, as a significant supplement to the existing means of characterizing soliton pulses, NFT is expected to be another fundamental optical processing method besides an oscilloscope (measuring pulse time domain information) and a spectrometer (measuring pulse frequency domain information).

A transonic, viscous nonlinear frequency domain Vortex Lattice Method for aeroelastic analyses

The Unsteady Vortex Lattice Method has interesting capabilities for nonlinear subsonic aeroelastic analyses. This paper aims to develop an aeroelastic framework based on the UVLM that is suitable for compressible, transonic and viscous unsteady flows. To achieve these modeling capabilities, the UVLM is first extended to the nonlinear frequency domain using the harmonic balance approach. Secondly, sectional corrections are applied from a steady 2D/2.5D database of aerodynamic forces computed with high-fidelity Euler/RANS flow solvers. The angle of attack coupling scheme on the lift force is complemented by a least-square procedure also coupling the pitching moment. Finally, an approximation of the retarded time is implemented in the influence kernel of the harmonic balance formulation of the UVLM to account for unsteady compressibility. The aerodynamic model is verified against time domain high-fidelity solutions with pitching airfoils in 2D and in 3D with a pitching constant chord NACA 0012 swept wing. Thereafter, the HB/LCO approach is applied with the frequency domain UVLM to 2D and 3D aeroelastic problems and compared against high-fidelity solutions. The proposed framework is capable of capturing strong nonlinear Limit Cycle Oscillation behaviors at high Mach numbers, as well as the flutter boundary for a wide range of Mach numbers while maintaining a low computational cost. As a result, the proposed framework could be of interest for preliminary design and Multi-Disciplinary Design (MDO) optimizations in the context of subsonic and transonic aircraft design.