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We introduce here an approach that presents the basics of quantum mechanics to electrical engineers using common matrix algebra and Fourier series knowledge. Designed to quickly impart a fundamental understanding, this strategy bypasses the complex mathematics typically required. Amidst the unfolding second quantum revolution, the accelerated development of quantum engineering in academia and industry underscores the urgent need for a skilled workforce. Scientific and technological fields like quantum computing, quantum sensing, and quantum communications are gaining significant momentum, necessitating the urgent involvement of electrical engineers skilled in management, design, manufacturing, and research. These professionals require foundational quantum mechanics knowledge to effectively integrate these principles with their existing technical skills in areas like automatic control theory and signal processing. Traditionally, educational methods have targeted physicists rather than engineers, often treating quantum mechanics as too abstract for practical engineering applications. However, the rise of quantum technology now demands the inclusion of engineers from diverse backgrounds. Our proposal offers this primer as an innovative, electrical engineering-focused educational tool. We strongly believe that our approach prepares engineers to make significant contributions to the rapidly expanding field of quantum technology.

The dual-loaded loop is a two-port antenna configured as two half-loops. Its advantage is the ability to sense two field components instead of the single component of a single-port loop. In this study, the theory of the dual-loaded loop is extended to cases for sensing arbitrarily located electric and magnetic dipole sources. New general expressions are presented for the tangential electric field on a loop resulting from electric and magnetic dipole sources. From these field expressions, closed-form approximations for the currents at the ports are obtained. The approximations are shown to be very accurate through simulation, but can degrade when the separation distance between the dipole source and loop is small. The worst discrepancy occurs when an electric dipole is close to and aligned with one of the ports. These expressions provide a benchmark for checking numerical and physical results for this class of sensor.

Prosthetic discrete controller relies on finite state machines to switch between a set of predefined task-specific controllers. Therefore the prosthesis can only perform a limited number of discrete locomotion tasks and need hours to tune the parameters for each user. In contrast, the continuous controller treats a gait cycle in a unified way. Thus it is expected to better facilitate normative biomechanics by providing a gait predictive model to contribute a non-switching controller that supports a continuum of tasks. Furthermore, a better method is to train a personalized trajectory prediction model suitable for personal characteristics according to personal walking data. This paper proposes a Gaussian process enhanced Fourier series (GPEFS) method to construct a gait prediction model that represents the human locomotion as a continuous function of phase, speed and slope. Firstly the joint trajectories are transformed into the Fourier coefficient space by least square method. Then the relationship between each Fourier coefficient and task input can be learned by multiple Gaussian process regression (GPRs) model respectively. Compared with directly using GPR to fit the joint trajectory under multi task, our method greatly reduces the computational burden, so as to meet the real-time application scenario. In addition, in Fourier coefficient space, the difference in all tasks between the Fourier coefficient of personal data and the one of statistical data follows the same trend. Therefore, a personalized prediction model is built to predict an individual’s kinematics over a continuous range of slopes and speeds given only one personalized task at level ground and normal speed. The experimental results show that the gait prediction model and the personalized prediction model are feasible and effective.

This study introduces a novel methodology based on the idea of double Fourier series and coil segmentation, performed based on governing equations, with harmonic magnetic field analysis of a double-sided air-cored superconducting linear synchronous motor for electrodynamic suspension train. This method can solve the harmonic magnetic field generated by arbitrarily shaped coils. First, with rectangular-shaped coils and race-track-shaped coils as examples, the process of calculating harmonic magnetic field using the proposed method is introduced comprehensively, and the influence of the end effect is also considered. Second, based on the solution results of the harmonic magnetic field, a modeling method that can quickly solve no-load superconducting flux linkage, no-load back EMF, and three-dimensional (3-D) electromagnetic forces without losing accuracy is presented, which is verified by finite element simulation. Finally, two static tests are designed. The effectiveness of the proposed method is verified by the test results of static thrust and static normal force. [ABSTRACT FROM AUTHOR]

Prosthetic discrete controller relies on finite state machines to switch between a set of predefined task-specific controllers. Therefore the prosthesis can only perform a limited number of discrete locomotion tasks and need hours to tune the parameters for each user. In contrast, the continuous controller treats a gait cycle in a unified way. Thus it is expected to better facilitate normative biomechanics by providing a gait predictive model to contribute a non-switching controller that supports a continuum of tasks. Furthermore, a better method is to train a personalized trajectory prediction model suitable for personal characteristics according to personal walking data. This paper proposes a Gaussian process enhanced Fourier series (GPEFS) method to construct a gait prediction model that represents the human locomotion as a continuous function of phase, speed and slope. Firstly the joint trajectories are transformed into the Fourier coefficient space by least square method. Then the relationship between each Fourier coefficient and task input can be learned by multiple Gaussian process regression (GPRs) model respectively. Compared with directly using GPR to fit the joint trajectory under multi task, our method greatly reduces the computational burden, so as to meet the real-time application scenario. In addition, in Fourier coefficient space, the difference in all tasks between the Fourier coefficient of personal data and the one of statistical data follows the same trend. Therefore, a personalized prediction model is built to predict an individual’s kinematics over a continuous range of slopes and speeds given only one personalized task at level ground and normal speed. The experimental results show that the gait prediction model and the personalized prediction model are feasible and effective. [ABSTRACT FROM AUTHOR]

Constant on-time current mode (COTCM) Buck converters are widely used in power management integrated circuit (ICs) for microprocessors. Small-signal models are necessary tools to design high-quality controllers. Existing models neglect output voltage ripples (OVRs) and spectrum extension caused by switching, which makes significant errors under high control bandwidth. This article adopts Fourier series to describe OVRs precisely. Then, influences of OVRs on COTCM are analyzed. Finally, spectrum coupling from current loop and voltage loop is incorporated to obtain a high-frequency model, and four universal analytical expressions in frequency domain are obtained with the aid of matrix calculation. Based on the proposed model and genetic algorithm, an optimal controller design method is developed. Simulation and experiment validate the accuracy of proposed model and the effectiveness of proposed design method. [ABSTRACT FROM AUTHOR]

This brief presents an event-based adaptive containment control scheme for nonlinear multi-agent systems with periodic disturbances and unknown coefficients. To decrease some unnecessary data transmissions, an improved event-triggered mechanism is introduced, i.e., a dynamically adjusted threshold is designed in the event-triggered condition. Then, a first-order sliding-mode differentiator is employed to address the “explosion of complexity” problem, and neural networks and fourier series expansion are combined to model the uncertain nonlinear dynamics subject to periodically time-varying disturbances. Stability analysis verifies that the containment errors are bounded, and a practical simulation is implemented to evaluate the validity of the developed scheme. [ABSTRACT FROM AUTHOR]

An overmodulation method is proposed for an in-wheel system where two motors are coupled to a sum gear. In the dual-motor dual-inverter single shaft systems, the output voltage magnitudes of two inverters are not the same in the overmodulation range due to the angle offset between two motors. In this article, to maintain torque balance in the overmodulation region, holding vectors are defined between adjacent vertices of two voltage hexagons. Around these vectors, the holding region is also defined by the holding angle. If a reference voltage vector is in the holding region, it is modulated to the holding vector; otherwise, it is modulated to the vector on the arc of inscribed circle. For a given the modulation index (MI), the holding angle is obtained based on the Fourier series expansion. The proposed method keeps the output voltages of two inverters the same even if two motors have the angle offset. Further, it has the characteristic of maintaining the linearity between the reference and output MI to the maximum MI. The proposed overmodulation method is demonstrated by simulation and experimental results. [ABSTRACT FROM AUTHOR]

Halbach arrays have been widely implemented in magnetic levitation systems. They concentrate the magnetic field over one side, and their magnetic flux density in the central region can be modeled. This article proposes a novel lookup table-free data-driven method to model the force and torque on a 2-D Halbach array when the magnet array is above a stationary coil. One critical contribution of this article is the rapid and accurate force and torque modeling when the coil is located near the edge of the 2-D magnet array. First, the area under the 2-D Halbach array is divided into a central region, edge regions, and corner regions. Then, nonlinear force and torque components are identified and modeled with a modified third-order Fourier series for force and torque modeling. The proposed model is implemented on an industrial server, and the average computation time is measured to be $2.3 ~\mu \text{s}$. This model is universal for symmetric coils, verified through experimental measurements with circular and square coils of different sizes. The measurement result agrees well with the proposed modeling method, showing that the proposed method is suitable for real-time control of the ironless planar motor. [ABSTRACT FROM AUTHOR]

In this brief, the problem of tracking control for uncertain nonlinear systems with periodic disturbances is studied. Based on the prescribed performance technology, two kinds of error transformation functions different from the traditional backstepping method are introduced, such that the proposed low-computation adaptive control method can ensure the boundedness of the signals of the closed-loop system. Meanwhile, the counter evidence method reveals that the system output can achieve accurate tracking. Compared with existing results, firstly, the complexity explosion problem is avoided without introducing a filter, making our result more applicable and less complex. Secondly, for the time-dependent periodic disturbances considered in the system, a function approximator based on Fourier series expansion can achieve accurate approximation with the least number of Gaussian basis functions. Comparative simulation results of the van der Pol oscillator illustrate the advantages of the proposed method. [ABSTRACT FROM AUTHOR]

Fast detection of hazardous objects in millimeter-wave personnel screening can increase the operating efficiency of secure environments. In airports, accurate automatic detection and classification of body-worn objects can reduce the number of pat-downs while keeping the transportation environment safe and secure. Since many benign objects, such as paper and leather, are lossy materials, being able to characterize them and set them aside from the secondary checks will significantly reduce the screening process time. In this article, we introduce an effective image-processing-based method for characterizing lossy materials that might be concealed under clothing at checkpoints. The method has been combined with a modified version of the previously developed algorithm that can be used specifically to characterize lossless materials. The proposed algorithm can automatically distinguish lossless materials from lossy ones and calculate their thickness and permittivities. Starting from the radar reconstructed image showing a cross section of the body, we extract the nominal body contour using the Fourier series, separate body, and object responses, categorize the object as lossy or lossless based on the depression and protrusion of the body contour, and, finally, predict possible values for the object’s permittivity and thickness. Our resulting classification is good, implying fewer nuisance alarms at checkpoints. [ABSTRACT FROM AUTHOR]

This letter presents a Space Vector Pulse Width Modulation (SVPWM) strategy for reducing the DC-link current harmonics in a multi– Voltage Source Inverter (VSI) topology with common DC-link bus. The DC current harmonic reduction is achieved by phase-shifting the PWM pattern of individual VSIs, with the inverters sharing the system total power. Simulation and experimental results are shown to validate the proposal. [ABSTRACT FROM AUTHOR]

The distributed parameters of a non-uniform transmission line (NTL) are assumed to depend on a finite set of unknown parameters, for example, their spatial Fourier series coefficients. The line equations are set up taking random voltage and current line loading into account with the random loading being assumed to be white Gaussian noise in the time and spatial variables. Bypassing over to the spatial Fourier series domain, these line stochastic differential equations (SDEs) are expressed as a truncated sequence of coupled stochastic differential equations for the spatial Fourier series components of the line voltage and current. The coefficients that appear in these stochastic differential equations are the spatial Fourier series coefficients of the distributed line parameters and these coefficients in turn are linear functions of the unknown parameters. By separating these complex stochastic differential equations into their real and imaginary part, the line equations become a finite set of SDEs for the extended state defined to be the real and imaginary components of the line voltage and current as well as the parameters on which the distributed parameters depend. The measurement model is assumed to be white Gaussian noise corrupted versions of the line voltage and current sampled at a discrete set of spatial points on the line and this measurement model can be expressed as a linear transformation of the state variables, i.e, of the spatial Fourier series components of the line voltage and current plus a white measurement noise vector. This work uses sparse matrix factorization using Kronecker product to implement the Fourier unitary transform. This work implements perturbation theory for non-uniform transmission line. The extended Kalman filter (EKF) equations are derived for this state and measurement model and our real timeline voltage and current and distributed parameter estimates show excellent agreement with the true values based on MATLAB simulations. The use of sparse matrix factorization using Kronecker product ease the mathematical complexity and provides compact representation. [ABSTRACT FROM AUTHOR]

This article presents a 3-D semi-analytical model of an axial-flux reluctance coupling. Thanks to the separation of variables method, Fourier series analysis and the convolution theorem (i.e., Cauchy's product), the salient-pole region is modelled by a spatially variable magnetic permeability. Additionally, an iterative algorithm is implemented to account for the magnetic saturation of the iron teeth. The results of the proposed model are compared with a previously published 2-D semi-analytical model, 3-D finite-element method and experimental results. The proposed method appears to be an appropriate tool for the design process of reluctance couplings in cases where the salient poles are saturated. [ABSTRACT FROM AUTHOR]

Fourier theory is the backbone of signal processing (SP) and communication engineering. It has been widely used in almost all branches of science and engineering in numerous applications since its inception. However, Fourier representations such as Fourier series (FS) and Fourier transform (FT) may not exist for some signals that fail to fulfill a predefined set of Dirichlet conditions (DCs). We note a subtle gap in explaining these conditions as available in popular SP literature. For example, original DCs require a signal to have bounded variations (BVs) over one time period for the convergence of FS, where there can be, at most, a countably infinite number of maxima and minima and, at most, a countably infinite number of discontinuities of finite magnitude. However, a large body of the literature replaces this statement with the requirements of a finite number of maxima and minima over one time period, and a finite number of finite discontinuities over one time period. Due to the latter, some signals fulfilling the original DCs are incorrectly perceived as not having convergent FS (CFS) representation. A similar problem holds in the description of DCs for the FT. Likewise, although it is easy to relate the first DC with the finite value of FS or FT coefficients, the relevance of second and third DCs, as specified in SP literature, is hard to assimilate. [ABSTRACT FROM AUTHOR]

To realize brushless excitation for an electrical excitation synchronous generator (EESG), a brushless-induced double electrical excitation synchronous generator (IDEESG) with dc excitation is investigated in this study. The static magnetic field is established by injecting dc into the stator excitation windings that are added in the stator slots. Rotor windings are divided into two parts: induction coils and rotor excitation winding. The induction coils cut the static magnetic field and provide dc current for the rotor excitation winding after the rectification. The direction of the currents in the induction coils is constant because of the half-wave rectification. The magnetic flux generated by the currents in the induction coils and rotor excitation winding is added in the air gap to induce the armature coils in the stator. In this study, the structure and the operating principle are examined. The frozen permeability method is adopted to study the influence of the currents in the induction coils and the rotor excitation winding on the magnetic field distribution. The harmonic content of currents in the induction coils is analyzed using the Fourier series form and the effect of the harmonics on the output voltage is also studied. A 1.5 kVA prototype is fabricated to verify the correctness of theoretical analysis and simulation. [ABSTRACT FROM AUTHOR]

Is it correct that the higher the detection accuracy of a single-phase shunt active power filter (SPSAPF) harmonic current detection (HCD) is, the more effective the HCD is? To answer the question, an interesting view correction for evaluating an SPSAPF HCD is proposed in this paper. The main points of the proposed view correction are as follows: The answer to the question is Yes when the load current changes periodically but No when the load current changes non-periodically. The proposed view correction also applies to a three-phase shunt active power filter; thus, it has general applicability. Its existence and feasibility are confirmed by experimental results. [ABSTRACT FROM AUTHOR]

A technique for trading off the main lobe width against sidelobe magnitude for any arbitrary window was reported in Lim et al. and subsequently, a fast convergence method for its implementation was proposed by the same authors. These methods require the computation of derivatives involving the evaluation of trigonometric and hyperbolic functions. In this paper, we show that the derivatives can be computed without evaluating trigonometric and hyperbolic functions if the window function is a sum of exponentials such as a Fourier series. [ABSTRACT FROM AUTHOR]

A new method extending the scope of the superalgebraically convergent 2-D wave diffraction algorithms is proposed. The principal tool is the construction of an infinitely smooth approximation to the boundary contour. The construction is based on the ideas of Tikhonov’s regularization to the stable summation of the Fourier series and the evaluation of unbounded operators. Both the algorithms for smoothing and the nonsaturated solutions for integral equations together provide the superalgebraic (faster than any algebraic) convergence. The comparison of the algorithms using the original (noninfinitely smooth) parameterization and the infinitely smooth one demonstrates the essential advantage of the latter over the former with respect to accuracy and time consumption. [ABSTRACT FROM AUTHOR]

The Fourier series is introduced as a transfer function (TF) in the artificial neural network (ANN) for parametric modeling of microwave filters in this letter. The reported pole-residue-based TF leads to an order-changing problem of input samples from vector fitting, which is usually solved with an order-tracking technique or data classification. The proposed Fourier series-based TF does not have to carry out the time-consuming operation because the only coefficient order can be determined for all input samples in an iterative process. Compared with the pole-residue-based TF, moreover, the ANN training involves a small number of TF coefficients in the proposed method. The predicted electromagnetic (EM) response is obtained from the coefficients of the ANN output. An example of the ultrawideband (UWB) filter is employed to verify the effectiveness of the Fourier series-based TF. [ABSTRACT FROM AUTHOR]

The magnetic field calculation for axial flux motors (AFMs) is always intricate and time-consuming. To this end, a fast quasi-three-dimensional (3D) analytical model is proposed in this paper for magnetic field prediction in AFMs. The 3D magnetic field problem can be simplified into a two-dimensional (2D) one by dividing the AFM into several annular slices in the radial direction. Then, for the first time, the harmonic modeling method (HMM) in Cartesian coordinates is adopted to solve the magnetic field in these slices cut from the AFM. The corresponding electromagnetic parameters of the AFM can be acquired subsequently. The critical step for the field prediction of using HMM in Cartesian coordinates is to adopt a variable substitution method when solving the partial differential equations. Next, the magnetic saturation of soft-magnetic material within AFMs is considered by adopting an iterative approach. Ultimately, the effectiveness of the proposed quasi-3D analytical model is validated by the nonlinear finite element analysis (FEA). The proposed analytical model is computationally efficient, which makes it suitable for the preliminary design of AFMs. [ABSTRACT FROM AUTHOR]

The stitch wire configuration is widely adopted for large-area IGBT chips. However, an inhomogeneous wire current density introduces uneven self-heating and nonuniform chip heating, which exacerbates the chip thermal stress. In this article, a multicellular electro-thermal model considering the stitch-bonding wires is derived to optimize the wire layout parameters. Furthermore, the current density alleviation of wire bonds is investigated to be the most sensitive and effective method to comprehensively mitigate the thermal nonequilibrium and local overheating. Consequently, an improved multitier layout is proposed to further achieve thermal stress suppression without any additional components and advanced materials. Finally, a triple-tier-bonded IGBT module with optimal design parameters is fabricated to validate the thermal mitigation performance. The prototype experimental results demonstrate that the modeling error is less than 3.0%. The multitier layout decreases the current density by 57.6%, hence, the maximum and average chip temperature are reduced by 21.8% and 12.4%, respectively. [ABSTRACT FROM AUTHOR]

Oscillations of grid-connected voltage source converter (VSC) usually reaches sustained state because of the limiters in controller. Describing function has been adopted to analyze the amplitude and frequency of the sustained oscillations, but high-order oscillation components caused by the limiter are ignored in previous literatures. This letter proposes an analysis method for sustained oscillations which considers high-order oscillation components. This method could obtain a more precise oscillation frequency and the amplitude of 1st, 2nd, and 3rd order components. The proposed method is verified by case studies and simulations in PSCAD/EMTDC. [ABSTRACT FROM AUTHOR]

This article presents a generalization of an analytical model of an axial-flux permanent-magnet machine to any magnet shape. It uses an existing model, which computes the 3-D magnetic-flux density by the separation of variables and a finite-difference method. The original magnet shape is modified by adding a radial dependency to the Fourier series description of permanent magnets (PM) magnetization. The model is then developed for a general complex magnet shape. As an example, the model will be computed for a circular magnet shape and will be compared with finite-element analysis. [ABSTRACT FROM AUTHOR]

In robotics, ergodic control extends the tracking principle by specifying a probability distribution over an area to cover instead of a trajectory to track. The original problem is formulated as a spectral multiscale coverage problem, typically requiring the spatial distribution to be decomposed as Fourier series. This approach does not scale well to control problems requiring exploration in search space of more than two dimensions. To address this issue, we propose the use of tensor trains, a recent low-rank tensor decomposition technique from the field of multilinear algebra. The proposed solution is efficient, both computationally and storagewise, hence making it suitable for its online implementation in robotic systems. The approach is applied to a peg-in-hole insertion task requiring full 6-D end-effector poses, implemented with a seven-axis Franka Emika Panda robot. In this experiment, ergodic exploration allows the task to be achieved without requiring the use of force/torque sensors. [ABSTRACT FROM AUTHOR]

In this article, we propose steady-state modeling of dc–dc converters driven by multiple pulsewidth modulation (PWM) signals. The proposed dc–dc converter modeling uses a switched state-space framework, and the switching signal discontinuities are represented by a Fourier series to obtain the average model. The advantage of the proposed modeling is that it is not dependent on the dc–dc converter topology, and the dimension of the state-space model does not increase with the number of storage devices. Additionally, the duty cycle and phase displacements among the driving PWM signals can be arbitrary and systematically modeled. The effectiveness of the proposed modeling is supported by simulation and experimental results. [ABSTRACT FROM AUTHOR]

This article considers the Nussbaum gain adaptive control issue for a type of nonlinear systems, in which some sophisticated and challenging problems, such as periodic disturbances, dead zone output, and unknown control direction are addressed. The Fourier series expansion and radial basis function neural network are incorporated into a function approximator to model time-varying-disturbed function with a known period in nonlinear systems. To deal with the problems of the dead zone output and unknown control direction, the Nussbaum-type function is recommended in the design of the control algorithm. Applying the Lyapunov stability theory and backstepping technique, the proposed control strategy ensures that the tracking error is pulled back to a small neighborhood of origin and all closed-loop signals are bounded. Finally, simulation results are presented to show the availability and validity of the analysis approach. [ABSTRACT FROM AUTHOR]

Motor drive systems with long feeder cables are widely used in mining and energy sectors, such as offshore oil and gas drilling. In recent decades, to prevent issues with electromagnetic interference, power quality standards have been defined for the 2–150 kHz frequency range. In order to comply with these standards, manufacturers need to design filters to avoid exceeding the thresholds set by the standards. An important aspect that needs to be considered is the accurate modeling of currents circulating through common-mode loops. This article addresses this modeling by using a mathematical approach. The power cable’s common-mode model is extracted from the measurement data using the finite-element method via finding the effective permittivity of the PVC materials. The common-mode noise sources, including the grid side voltage through the front-end diode rectifier and the output voltage through the rear-end inverter, are both modeled by extracting the Fourier series calculations. Consequently, noise emissions circulating through different common-mode loops are analytically modeled. Through the proposed modeling strategy, the harmonic spectrum of resonances can be precisely analyzed. The results are validated through simulation and experimental data. [ABSTRACT FROM AUTHOR]

This article develops a new closed-form analytical solution to the harmonic spectrum of the full-bridge (FB) modular multilevel converter (MMC) with phase shifted carrier pulse width modulation. It considers FB-MMC operation in boost mode where the negative-voltage states of the FB submodules (SMs) are utilized to extend the ac operating voltage range and/or reduce the dc link voltage which is known to reduce the energy storage requirement. The solution is based on double Fourier series expansion in two variables. The harmonic distribution of the output voltage is analyzed and the effects of the modulation index and the number of SMs on the output voltage harmonics are revealed. The influence of the upper/lower arm carrier phase shift angle is also investigated. Using the analysis, selection of the number of SMs, the modulation index and the upper/lower arm carrier phase shift angle are specified for output voltage harmonic minimization. The findings are verified by simulation and experimental results. [ABSTRACT FROM AUTHOR]

This paper contributes by developing an univariate and multivariate harmonic decomposition methodology to model time series.The models are stated in a state space representation derived from a Fourier series analysis to describe an arbitrary signal. The frequency values of the harmonic content are used to define state variables in order to describe a signal through a time-varying linear state space model, which serves to synthesize an optimal state observer (Kalman-Bucy filter). Once the observer converges and the states (harmonics) become constant, the observer model can be used to predict the signal, i.e., a time series forecasting can be performed.The preocedure can be developed for the univariate or multivariate case of time series modeling, where in the last one, a statistical analysis is used to determine which variables should be taken into account to obtain a more accurate model. The proposed modeling approach is successfully applied for the modeling and forecast of the time series of electrical power demand and a wind/solar profile. [ABSTRACT FROM AUTHOR]

This work continues the development of the ray-tracing method of de Jong (2021) for computing the scattered fields from metasurfaces characterized by locally periodic reflection and transmission coefficients. In this work, instead of describing the metasurface in terms of scattering coefficients that depend on the incidence direction, its scattering behavior is characterized by the surface susceptibility tensors that appear in the generalized sheet transition conditions (GSTCs). As the latter quantities are constitutive parameters, they do not depend on the incident field and, thus, enable a more compact and physically motivated description of the surface. The locally periodic susceptibility profile is expanded into a Fourier series subject to a spatially varying phase parameter, and the GSTCs are rewritten in a form that enables them to be numerically solved for the reflected and transmitted surface fields. The phase parameter can either be determined from a prescribed surface transformation or extracted from known surface susceptibilities. A method for the extraction of this phase parameter from a susceptibility profile using a spatial variant of the short-time Fourier transform (STFT) is proposed. The scattered field at arbitrary detector locations is constructed by evaluating critical-point contributions of the first and second kinds using a forward ray-tracing (FRT) scheme. The accuracy of the resulting framework has been verified with an integral equation-based boundary element method (BEM)-GSTC full-wave solver for a variety of examples, such as a periodically modulated metasurface, a metasurface diffuser, and a beam collimator. [ABSTRACT FROM AUTHOR]

This article deals with 2-D modeling of coupled vibrations of finite piezoelectric resonators. A general solution for all the physical quantities in the Cartesian and cylindrical coordinate systems is deduced from the governing equations by expansion in series summation of trigonometric functions of thickness coordinate and trigonometric or Bessel functions of the lateral one. The essential difference between this model and the earlier ones is that instead of expressing mainly in the thickness coordinate and integration through the thickness, the solutions are expressed in the form of double Fourier series augmented by single Fourier or Fourier–Bessel series, which contributes to better satisfy the mechanical and electrical boundary conditions. The dynamic stiffness matrix of the system is developed. Electrical impedances of a typical piezoelectric parallelepiped under stress-free and symmetrical loading conditions and its frequency spectrum for different width-to-thickness ratios are calculated using our model as well as by the finite element method. A comparison shows an excellent agreement. Finally, theoretical and measured electrical impedances of a piezoelectric parallelepiped and a piezoelectric disk are compared and discussed. The 2-D theoretical model proposed here is shown to be accurate and efficient for coupled vibration analysis of piezoelectric resonators and is applicable for any set of finite dimensions and crystal symmetry. [ABSTRACT FROM AUTHOR]

Multi-scale processing is essential in image processing and computer graphics. Halos are a central issue in multi-scale processing. Several edge-preserving decompositions resolve halos, e.g., local Laplacian filtering (LLF), by extending the Laplacian pyramid to have an edge-preserving property. Its processing is costly; thus, an approximated acceleration of fast LLF was proposed to linearly interpolate multiple Laplacian pyramids. This paper further improves the accuracy by Fourier series expansion, named Fourier LLF. Our results showed that Fourier LLF has a higher accuracy for the same number of pyramids. Moreover, Fourier LLF exhibits parameter-adaptive property for content-adaptive filtering. [ABSTRACT FROM AUTHOR]

This article presents a high-fidelity analytical solution and a fast integrated optimization method for vernier machines. First, a harmonic modeling method (HMM) is adopted to obtain the magnetic field distribution of vernier machines. Particularly, the stator teeth of vernier machines are divided into several blocks to take account of the local magnetic saturation of soft-magnetic material. Then, the electromagnetic parameters, such as the average torque, torque ripple, and efficiency, can be calculated via the analytical model. Next, the proposed harmonic model is combined with the nondominated sorting genetic algorithm II (NSGA-II) to determine a multiobjective optimal design for the studied vernier machine. This integrated optimization method can save computation time, because the data interaction process between the finite-element analysis (FEA) software and the optimization software is eliminated. Finally, the performances of the optimal case are verified by both FEA and experiments with the prototype. [ABSTRACT FROM AUTHOR]

Fault detection of a rotating rectifier for a wound-rotor synchronous starter/generator (WRSSG) without a rotor position sensor in the stationary state is necessary for a successful engine start. Based on high-frequency (HF) voltage injection, a novel fault detection method of the rotating rectifier for the WRSSG in the stationary state is proposed. The rotating HF voltage is imposed on the stator windings of the main machine, and the HF feature current signal extracted on the stator windings of the main exciter is used for fault detection. In this article, the HF current signal in the main exciter with the rotating rectifier under different working conditions is analyzed first. To obtain the HF response current on the stator windings of the main exciter, the HF model of the WRSSG is analyzed. Through the Fourier series, the HF feature current signal together with fault detection is achieved. Compared with the existing fault detection methods, the proposed method shows no dependency on the rotor position information. Experimental results verify the feasibility and effectiveness of this method. [ABSTRACT FROM AUTHOR]

Noises from the measurement sensors are inevitable in radar cross Section testing due to the thermal agitation of electrons in imperfect conductors. Existing methods represented by wavelet threshold usually regard the measured data as a stationary stochastic signal, ignoring the inherent influence of the target under test, which inevitably removes the signal’s component when noise increases. This paper proposes a novel perspective on 2-D radar cross Section measurement denoising, considering the target’s inherent scattering characteristics (ISC). In the proposed method, the noise and the target are firstly separated as far as possible in the generalized Fourier series domain while the target’s component is all preserved. Then, the noise is further suppressed by the scattered field reconstruction of the Hankel function. Finally, a metal sphere being a calibrator is introduced to improve the denoising ability. Both simulations and experimental studies demonstrate the superiority of our method compared with existing algorithms. Results indicate that the proposed method can achieve higher accuracy. [ABSTRACT FROM AUTHOR]

An aircraft transition connects two flight conditions and is a fundamental component of aerospace operations. For achieving a seamless transition that accurately connects two steady flights, a hierarchical parameterization method is developed in this article for generating smooth flight trajectories satisfying hard boundary constraints on controls and control derivatives of all orders. The proposed work is based on a trigonometric series parameterization of control variables and hierarchically parameterizes the series coefficients with flat and logistic functions, leading to a new set of coefficients and a formulation that inherently guarantees the desired conditions. The new set of coefficients can be determined by optimization methods and can be integrated in existing methods with the advantage of streamlining the problem formulation. Simulation studies including comparisons demonstrate the effectiveness and performance of the proposed method. [ABSTRACT FROM AUTHOR]

This article presents an improved analytical spatial harmonics subdomain (SHSD) model for analyzing the influence of individual spatial harmonics, in stator magneto-motive forces (MMFs), on the performance of multiphase cage rotor induction motors (CRIMs). The proposed SHSD model is an extension of conventional techniques that consider each MMF spatial harmonic, caused by stator slots with tooth-tips, to be individual excitations when quantitatively analyzing the resulting physical effects. The solution domain was divided into four subdomains (SDs) in 2-D polar coordinates, including 1) rotor bars described by the Helmholtz equation; 2) air gaps; 3) slot openings described by Laplace’s equation; 4) stator slots represented by pure forced vibration equations. Current density in the stator structure was decomposed in a Fourier series of position angles to obtain MMF spatial harmonics. This produced a set of pure forced vibration equations in the stator slots, which were first solved in 2-D polar coordinates rather than the typical Poisson’s equation. This approach establishes a relationship between electromagnetic performance and stator parameters, for further optimization of IMs and analysis of electromagnetic vibrations. The proposed analytical model was validated using a series of finite element simulations, which exhibited high accuracy and computational efficiency. [ABSTRACT FROM AUTHOR]

This paper combines the use of multi-phase configurations and current harmonic injection methods to achieve significantly improved performance for doubly salient synchronous reluctance machines (DS-SRMs). In order to understand the torque production mechanism of multi-phase DS-SRMs with current harmonic injection, some general analytical torque models have been developed. The models are based on Fourier Series analysis of self- and mutual-inductances. It has been established that with current harmonic injection, the torque ripple of both 5-phase and 6-phase DS-SRMs can be significantly reduced and the average torque can be enhanced. It contrast, harmonic injection always has a detrimental impact on 4-phase machines. The investigations of losses and dynamic performance with current harmonic injection for multi-phase machine have also been carried out and demonstrated that the proposed method can improve the efficiency in constant torque region and maintain comparable performance to fundamental current supply in the flux weakening region. Experimental validation based on single layer, 6-phase, DS-SRM has been performed. [ABSTRACT FROM AUTHOR]

Objective: To investigate the importance of membrane charge oscillations and redistribution in multi-compartmental ultrasonic neuromodulation (UNMOD) intramembrane cavitation models. Methods: The Neuronal Intramembrane Cavitation Excitation (NICE) model and multiScale Optimized model of Neuronal Intramembrane Cavitation (SONIC) of UNMOD are compared for a nanoscale multi-compartmental and point neuron approximation of the bilayer sonophore and surrounding proteins. The temporal dynamics of charge oscillations and their effect on the resulting voltage oscillations are investigated by fourier series analysis. Results: Comparison of excitation thresholds and neuronal response between nanoscale multi-compartmental and point models, implemented in the SONIC and NICE framework, demonstrates that the explicit modeling of fast spatial charge redistribution is critical for an accurate multi-compartmental UNMOD-model. Furthermore, the importance of modeling partial protein coverage is quantified by the excitability thresholds. Subsequently, we establish by fourier analysis that these charge oscillations are slowly changing in time. Conclusion: Fast charge redistribution significantly alters neuronal excitability in a multi-compartmental nanoscale UNMOD-model. Also the mutual exclusivity between protein and sonophore coverage should be taken into account, when simulating the dependency of neuronal excitability on coverage fractions. Charge oscillations are periodic and their fourier components change on a slow timescale. Furthermore, the resulting voltage oscillations decrease in energy with overtone number, implying that an extension of the existing multiscale model (SONIC) to multi-compartmental neurons is possible by taking into account a limited number of fourier components. Significance: First steps are taken towards a morphologically realistic and computationally efficient UNMOD-model, improving our understanding of the underlying ultrasonic neuromodulation mechanisms. [ABSTRACT FROM AUTHOR]

The application of frequency offsets to the elements of a conventional phased array with variable phase shifters (VPSs) leads to frequency diverse arrays (FDAs) with the ability to provide range-angle spatial focusing. In this letter, we propose an innovative approach to FDA using switched time-modulated arrays (TMAs) instead of VPSs. The time modulation efficiency of the combined FDA-TMA approach is over 94% when using Kaiser windows to determine the frequency offsets. Such windows have the advantage of flexibly handling the tradeoff between the beam collection efficiency and the half power beamwidth without the need of difficult optimizations. [ABSTRACT FROM AUTHOR]