Search Results (474)

This paper presents an open-source time-dependent three-dimensional scalar photorefractive beam propagation model (PRProp3D) based on the well-known split-step method. The angular spectrum method is used for the diffractive steps, and the nonlinearities accumulated at the end of each diffractive step are applied using spatially varying phase screens. Comparisons with previously published experimental results are given for image amplification, photorefractive amplified scattering (fanning) and photorefractive screening solitons. Artifacts can be mitigated by use of step sizes less than 5~10 micrometers and by careful choice of the transverse computation grid size to ensure adequate sampling. Wraparound effects associated with the use of discrete Fourier transforms are mitigated by apodization and beam centering. Full article

In this paper, we describe the associative and commutative algebra or the (2,2)-model of quaternions with application in color image enhancement. The method of alpha-rooting, which is based on the 2D quaternion discrete Fourier transform (QDFT) is considered. In the (2,2)-model, the aperiodic convolution of quaternion signals can be calculated by the product of their QDFTs. The concept of linear convolution is simple, that is, it is unique, and the reduction of this operation to the multiplication in the frequency domain makes this model very attractive for processing color images. Note that in the traditional quaternion algebra, which is not commutative, the convolution can be chosen in many different ways, and the number of possible QDFTs is infinite. And most importantly, the main property of the traditional Fourier transform that states that the aperiodic convolution is the product of the transform in the frequency domain is not valid. We describe the main property of the (2,2)-model of quaternions, the quaternion exponential functions and convolution. Three methods of alpha-rooting based on the 2D QDFT are presented, and illustrative examples on color image enhancement are given. The image enhancement measures to estimate the quality of the color images are described. Examples of the alpha-rooting enhancement on different color images are given and analyzed with the known histogram equalization and Retinex algorithms. Our experimental results show that the alpha-rooting method in the quaternion space is one of the most effective methods of color image enhancement. Quaternions allow all colors in each pixel to be processed as a whole, rather than individually as is done in traditional processing methods. Full article

The previously proposed cascaded inverse fast Fourier transform/fast Fourier transform (IFFT/FFT)-based point-to-multipoint (P2MP) flexible optical transceivers have the potential to equip future intensity modulation and direct detection (IMDD) optical access networks with excellent flexibility, adaptability, scalability and upgradability. However, due to their cascaded IFFT-based multi-channel aggregations, P2MP flexible transceivers suffer high peak-to-average power ratios (PAPRs). To address the technical challenge, this paper proposes a novel P2MP flexible optical transceiver, which uses a cascaded discrete Fourier transformation-spread (DFT-Spread) IFFT/FFT-based multi-channel aggregation/de-aggregation and standard signal clipping to jointly reduce its PAPRs. The upstream performances of the proposed transceivers are numerically explored in a 20 km IMDD upstream passive optical network (PON). The results indicate that the proposed transceiver’s PAPRs are mainly dominated by the size of the last IFFT operation of the multi-channel aggregation, and are almost independent of modulation format and channel count. Compared to conventional cascaded IFFT/FFT-based P2MP transceivers with and without clipping operations, the proposed DFT-Spread P2MP transceivers can reduce PAPRs by 2.6 dB and 3.5 dB, respectively, for a final IFFT operation size of 1024. More significant PAPR reductions are achievable when the last IFFT operation size is increased further. As a direct result, compared to conventional P2MP transceivers adopting clipping operations only, the proposed transceiver can improve upstream receiver sensitivities by >1.9 dB and the aggregated upstream transmission capacities by >14.1%. Such aggregated upstream transmission capacity enhancements are independent of channel count and become more pronounced for longer transmission distances. Full article

In this paper, algorithms for calculating different types of generalized trigonometric and hyperbolic functions are developed and presented. The main attention is focused on the Ateb-functions, which are the inverse functions to incomplete Beta-functions. The Ateb-functions can generalize every kind of implementation where trigonometric and hyperbolic functions are used. They have been successfully applied to vibration motion modeling, data protection, signal processing, and others. In this paper, the Fourier transform’s generalization for periodic Ateb-functions in the form of Ateb-transform is determined. Continuous and discrete Ateb-transforms are constructed. Algorithms for their calculation are created. Also, Ateb-transforms with one and two parameters are considered, and algorithms for their realization are built. The quantum calculus generalization for hyperbolic Ateb-functions is constructed. Directions for future research are highlighted. Full article

In this study, a class of nonlinear heterogeneous reaction–diffusion system (RDS) has been considered that arises in modeling epidemiological interactions, environmental sciences, and chemical and ecological systems. Numerical and analytic solutions for this kind of variable medium nonlinear RDS are challenging. This article developed a few highly accurate numerical schemes for such problems. For the spatial integration of the heterogeneous RDS, a few finite difference schemes, a Bernstein collocation scheme, and a Fourier transform scheme were employed. The stability and accuracy analysis of the spectral schemes were studied to confirm the order of convergence of the approximation. A few methods of lines were then used for the temporal integration of the resulting semidiscrete model. It was confirmed theoretically that the spectral/pseudo-spectral method is very efficient and highly accurate for such a model. A fast and efficient solver for the resulting full discrete system is highly desired. A Newton–GMRES–Multigrid solver was applied for the resulting full discrete system. It is demonstrated in tabular form that a multigrid accelerated Newton–GMRES solver outperforms most linear solvers for such a model. Full article

The clumping index (CI) is a key structural parameter that quantifies the nonrandomness of the spatial distribution of vegetation canopy leaves. Investigating seasonal variations in the CI is crucial, especially for estimating the leaf area index (LAI) and studying global carbon and water cycles. However, accurate estimations of the seasonal CI have substantial challenges, e.g., from the need for accurate hot spot measurements, i.e., the typical feature of the bidirectional reflectance distribution function (BRDF) shape in the current CI algorithm framework. Therefore, deriving a phenologically simplified stable CI product from a high-frequency CI product (e.g., 8 days) to reduce the uncertainty of CI seasonality and simplify CI applications remains important. In this study, we applied the discrete Fourier transform and an improved dynamic threshold method to estimate the start of season (SOS) and end of season (EOS) from the CI time series and indicated that the CI exhibits significant seasonal variation characteristics that are generally consistent with the MODIS land surface phenology (LSP) product (MCD12Q2), although seasonal differences between them probably exist. Second, we divided the vegetation cycle into two phenological stages based on the MODIS LSP product, ignoring the differences mentioned above, i.e., the leaf-on season (LOS, from greenup to dormancy) and the leaf-off season (LFS, after dormancy and before greenup of the next vegetation cycle), and developed the phenologically simplified two-stage CI product for the years 2001–2020 using the MODIS 8-day CI product suite. Finally, we assessed the accuracy of this CI product (RMSE = 0.06, bias = 0.01) via 95 datasets from 14 field-measured sites globally. This study revealed that the CI exhibited an approximately inverse trend in terms of phenological variation compared with the NDVI. Globally, based on the phenologically simplified two-stage CI product, the CI_LOS is smaller than the CI_LFS across all land cover types. Compared with the LFS stage, the quality for this CI product is better in the LOS stage, where the QA is basically identified as 0 and 1, accounting for more than ~90% of the total quality flag, which is significantly higher than that in the LFS stage (~60%). This study provides relatively reliable CI datasets that capture the general trend of seasonal CI variations and simplify potential applications in modeling ecological, meteorological, and other surface processes at both global and regional scales. Therefore, this study provides both new perspectives and datasets for future research in relation to CI and other biophysical parameters, e.g., the LAI. Full article

We discuss determining a finite sample linear time-invariant (FS-LTI) system’s impulse response function, h[n], in the frequency domain when the input testing function is a uniform window function with a width of L and the output is limited to a finite number of effective samples, M. Assuming that the samples beyond M are all zeros, the corresponding infinite sample LTI (IS-LTI) system is a marginally stable system. The ratio of the discrete Fourier transforms (DFT) of the output to input of such an FS-LTI system, H0[k], cannot be directly used to find h[n] via inverse DFT (IDFT). Nevertheless, H0[k] contains sufficient information to determine the system’s impulse response function (IRF). In the frequency-domain approach, we zero-pad the output array to a length of N. We present methods to recover h[n] from H0[k] for two scenarios: (1) N≥max(L,M+1) and N is a coprime of L, and (2) N≥L+M+1. The marginal stable system discussed here is an artifact due to the zero-value assumption on unavailable samples. The IRF obtained applies to any LTI system up to the number of effective data samples, M. In demonstrating the equivalence of H0[k] and h[n], we derive two interesting DFT pairs. These DFT pairs can be used to find trigonometric sums that are otherwise difficult to prove. The frequency-domain approach makes mitigating the effects of interferences and random noise easier. In an example application in radar remote sensing, we show that the frequency-domain processing method can be used to obtain finer details than the range resolution provided by the radar system’s transmitter. Full article

Mud pulse telemetry (MPT) systems are widely recognized for their effectiveness and are most commonly used to transmit downhole data to the surface in real time. These data facilitate the drilling process and make it more cost-efficient. In MPT, the mud channel presents a challenging communication environment, primarily due to various sources of noises, with pump noise being the most dominant. In this paper, a noise cancellation method based on discrete Fourier transform (DFT) is proposed for demodulation under a low signal-to-noise ratio, eliminating the pump noise generated by two pumps with a single sensor during drilling. The method employs DFT to estimate the noise spectrum, subtracts noises from the received signal, and performs an inverse transformation to reconstruct the original signal estimation. The effectiveness of the proposed method is evaluated through a simulation analysis and field experiments. The simulation results indicate that the major components of multiple pump noises could be successfully eliminated. The field experiment results demonstrate that the demodulation of the received data achieves advanced data rate communication and a low bit error rate (BER) in a 3000 m drilling system. Full article

This paper presented an extended double-subsegment discrete Fourier transform (DS-DFT) algorithm as a tool for the fine spectral estimation of high-noise environments, which was previously effective in low-noise scenarios, and as such, its application to the analysis of noisy signals observed by a satellite-based interferometer was investigated. The observation of satellite-borne Doppler asymmetric spatial heterodyne spectroscopy (DASH) was first simulated to obtain the signals of low- and high-noise levels; then, a practical criterion to classify noise levels in the interferograms based on the DS-DFT results was introduced and validated by calculating the SNR. For high-noise signals, DS-DFT remains robust by employing phase differences and amplitude ratios for fine frequency estimation. Full article

This paper presents an innovative numerical technique for specific classes of stochastic heat equations. Our approach uniquely combines a sixth-order compact finite difference algorithm with fast discrete Fourier transforms. While traditional discrete sine transforms are effective for approximating second-order derivatives, they are inadequate for first-order derivatives. To address this limitation, we introduce an innovative variant based on exponential transforms. This method is rigorously evaluated on two forms of stochastic heat equations, and the solutions are compared with those obtained using the established stochastic ten non-polynomial cubic-spline method. The results confirm the accuracy and applicability of our proposed method, highlighting its potential to enhance the numerical treatment of stochastic heat equations. Full article

The strong development of distributed energy sources has become one of the most important measures for low-carbon development worldwide. With a significant quantity of photovoltaic (PV) power generation being integrated to the grid, accurate and efficient prediction of PV power generation is an essential guarantee for the security and stability of the electricity grid. Due to the shortage of data from PV stations and the influence of weather, it is difficult to obtain satisfactory performance for accurate PV power prediction. In this regard, we present a PV power forecasting model based on a Fourier graph neural network (FourierGNN). Firstly, the hypervariable graph is constructed by considering the electricity and weather data of neighbouring PV plants as nodes, respectively. The hypervariance graph is then transformed in Fourier space to capture the spatio-temporal dependence among the nodes via the discrete Fourier transform. The multilayer Fourier graph operator (FGO) can be further exploited for spatio-temporal dependence information. Experiments carried out at six photovoltaic plants show that the presented approach enables the optimal performance to be obtained by adequately exploiting the spatio-temporal information. Full article

With the popularization of power electronic equipment, the problem of harmonic pollution has become more and more prominent, posing a serious threat to the safe operation of power systems. In order to improve the stability and efficiency of the power system, the broadband measurement of harmonics has become a key direction of research. In this paper, a novel broadband harmonic measurement method is proposed, which combines the electric field sensing technique and the TCW add-window discrete Fourier transform technique. The amplification gain coefficient deviation of the measurement system is less than 3 dB in both steady-state and transient excitation signal test experiments. The measurement system can maintain a stable and continuous output in a wide frequency band within the range of MHz, which can effectively detect the harmonic components and provide an effective technical means for the monitoring of harmonics in the power system. Full article

The Fourier transform is widely accepted as the time-to-frequency conversion procedure, although it has some limitations. Currently, measurements in the time domain are usually transient (non-periodic waveforms) within a finite window time and discrete (non-continuous) sampled signals. The accuracy of the Fourier transform decreases as the window time and sampling frequency decrease. This is where the wavelet transform proves to be a valuable tool in this analysis. This paper presents a novel method for estimating the complex electrical impedance of power transformers by analyzing transient electrical signals with the continuous wavelet transform. The great importance of knowing the complex electrical impedance of the transformer is that it allows knowing the state and condition of the internal parts, such as the core and the windings, whose behavior depends on the frequency with which the transformer is fed. The wavelet transform is employed in the proposed method to improve the analysis of the frequency response (FRA), following the same procedure commonly used with the Fourier transform. The proposed method is validated by performing an experimental test on a 28 MVA power transformer. The results show that the new method using the continuous wavelet transform is a power tool that enhances the extraction of the total electrical impedance curve (magnitude–phase) compared to the Fourier transform. This enables real-time frequency response analysis in transformers, facilitating accurate diagnosis. Full article

Speech enhancement technology seeks to improve the quality and intelligibility of speech signals degraded by noise, particularly in telephone communications. Recent advancements have focused on leveraging deep neural networks (DNN), especially U-Net architectures, for effective denoising. In this study, we evaluate the performance of a 6-level skip-connected U-Net constructed using either conventional convolution activation blocks (CCAB) or innovative global local former blocks (GLFB) across different processing domains: temporal waveform, short-time Fourier transform (STFT), and short-time discrete cosine transform (STDCT). Our results indicate that the U-Nets can receive better signal-to-noise ratio (SNR) and perceptual evaluation of speech quality (PESQ) when applied in the STFT and STDCT domains, with comparable short-time objective intelligibility (STOI) scores across all domains. Notably, the GLFB-based U-Net outperforms its CCAB counterpart in metrics such as CSIG, CBAK, COVL, and PESQ, while maintaining fewer learnable parameters. Furthermore, we propose domain-specific composite loss functions, considering the acoustic and perceptual characteristics of the spectral domain, to enhance the perceptual quality of denoised speech. Our findings provide valuable insights that can guide the optimization of DNN designs for causal speech denoising. Full article

In this paper, we study the Caputo–Hadamard time-space fractional diffusion equation, where the Caputo derivative is defined in the temporal direction and the Hadamard derivative is defined in the spatial direction separately. We first use the Laplace transform and the modified Fourier transform to study the analytical solution of the Cauchy problem. Then, using the Galerkin finite element method in space, we generate a semi-discrete scheme and study the convergence analysis. Furthermore, using the L1 scheme of the Caputo derivative in time, we construct a fully discrete scheme and then discuss the stability and error estimation in detail. Finally, the numerical experiments are displaced to verify the theoretical results. Full article