Frequency-domain Model Research Articles

A Study on the Frequency-Domain Black-Box Modeling Method for the Nonlinear Behavioral Level Conduction Immunity of Integrated Circuits Based on X-Parameter Theory.

During circuit conduction immunity simulation assessments, the existing black-box modeling methods for chips generally involve the use of time-domain-based modeling methods or ICIM-CI binary decision models, which can provide approximate immunity assessments but require a high number of tests to be performed when carrying out broadband immunity assessments, as well as having a long modeling time and demonstrating poor reproducibility and insufficient accuracy in capturing the complex electromagnetic response in the frequency domain. To address these issues, in this paper, we propose a novel frequency-domain broadband model (Sensi-Freq-Model) of IC conduction susceptibility that accurately quantifies the conduction immunity of components in the frequency domain and builds a model of the IC based on the quantized data. The method provides high fitting accuracy in the frequency domain, which significantly improves the accuracy of circuit broadband design. The generated model retains as much information within the frequency-domain broadband as possible and reduces the need to rebuild the model under changing electromagnetic environments, thereby enhancing the portability and repeatability of the model. The ability to reduce the modeling time of the chip greatly improves modeling efficiency and circuit design. The results of this study show that the "Sensi-Freq-Model" reduces the broadband modeling time by about 90% compared to the traditional ICIM-CI method and improves the normalized mean square error (NMSE) by 18.5 dB.

Comparison of time-domain and frequency-domain models for vibration prediction of a rail transit viaduct paved with floating slab track

Noise from rail transit viaducts often has a negative effect on surrounding buildings and nearby residents. To reduce the bridge vibration and radiated noise, floating slab tracks have been widely adopted in rail transit viaducts. To calculate the vibration of coupled track-bridge systems, both time-domain and frequency-domain methods can be applied although their relative performance is not very clear. This study aims to compare the two approaches and then provide some guidelines in choosing the appropriate method for predicting the vibration. The principle and methodology of the two calculation methods are firstly introduced, and the models for the train, floating slab track and bridge are developed using similar parameters. To further improve the efficiency and accuracy of the frequency-domain method, a half period method and a weighted average method are proposed to calculate the average responses of a certain point on the rail, floating slab and bridge to approximate the response during the pass-by. An indirect method is used to estimate the wheel–rail combined roughness from the measured rail acceleration when the train is running on the bridge, and compared with the direct measurement rail roughness. For the vibration of the bridge and floating slab, comparisons are made between results obtained from the time-domain and frequency-domain methods with different train speeds, and between results from experiment and simulation with different roughness. It is found that the wheel–rail contact forces and other structural responses from the two approaches show good consistency in the frequency region above 20 Hz. It is shown that a good approximation of the response during the pass-by can be obtained using the frequency-domain method by adopting the half period average or a simplified weighted average of two wheel position cases. When using the measured roughness and estimated roughness, the simulated vibration of the floating slab and bridge match well with the experimental results, and the indirect method can be used to modify direct measurement roughness in lower frequency regions. In the vibration prediction, the rail vibration or roughness, and other parameters in the vehicle–track–bridge system, should be measured accurately to ensure high reliability.

Cascaded framework for earthquake building damage detection combining spatial and frequency domain feature integration

Abstract. Building collapse is a major cause of casualties after an earthquake, so accurately extracting building damage information is critical for post-earthquake assessment and rescue. Currently, most deep learning methods focus on the end-to-end detection of building collapse. However, in real-world earthquake scenarios, the end-to-end computational process often lacks flexibility and struggles to meet the requirements of rapid emergency response. To address this issue, this paper proposes a cascaded framework that combines pre-earthquake building extraction and post-earthquake building damage classification. The proposed framework includes two sections: (1) Progressive building semantic segmentation model in the joint frequency domain. This model is designed to accurately extract buildings prior to an earthquake, with the goal of minimizing error propagation throughout the cascading process. The model addresses the spatial similarity of buildings under complicated backgrounds, as well as the high internal heterogeneity of buildings, by utilizing frequency domain techniques. It compensates for the shortcomings of traditional models in terms of incomplete information extraction through the effective integration of global and local information. Finally, the model employs edge priors for edge regularization. (2) Rapid building damage classification process. Based on the accurate building extraction results, a fast and efficient classification process is developed. This process uses a simple and lightweight classification network to effectively extract building damage information caused by the earthquake. The superiority of the proposed framework is validated through comparison with traditional cascading architectures and end-to-end models. The results show that the cascading framework not only provides accurate pre-earthquake building extraction, but also enables efficient and accurate post-earthquake damage classification, which meets the requirements of rapid post-earthquake emergency response. This balance of accuracy and speed is essential for effective disaster management and recovery.

Inverse modeling of frequency domain-based one-dimensional soil water flow in layered soils

Soils are heterogeneous at multiple scales. Estimates of spatially varying saturated hydraulic conductivity (Ks) of soils dictate the resolution of modeling water flux based on the Richardson-Richards equation (RRE), but direct measurements of Ks everywhere in a field are practically impossible. As a result, this study develops an inverse approach to estimate spatially varying Ks utilizing soil moisture observations driven by periodic weather variability at different frequencies. Using a numerical solution to vertical, one-dimensional RRE based on Gardner-Kozeny (GK) model in a heterogeneous soil with periodic flux, we investigate the spatial cross-correlation between Ks and observations (the amplitude or phase shift) of soil moisture fluctuation at different frequencies without high computational cost in the conventional time-domain model. These correlation patterns vary with the spatial location and frequency, suggesting that soil moisture fluctuations at different frequencies at one monitoring location carry non-redundant information about the heterogeneous distribution of Ks. Guided by cross-correlation maps, several inverse experiments reveal the effectiveness of multi-frequency data of soil moisture fluctuation for mapping the heterogeneous distribution of Ks. Monte Carlo simulations suggest that multi-frequency data can provide non-redundant and useful information about the estimation of heterogeneous Ks. Synthetic data based on a commonly-applied nonlinear van Genuchten-Mualem (VG) model is then tested in our inversion algorithm. The results indicate that the spatial pattern of the inverted GK Ks is very similar to that of the VG Ks, although these two parameters are inherently not identical since they are used in two different models. In addition, the inverted GK Ks can successfully predict the soil moisture fluctuation of frequencies that were not used in the inversion. Despite having no field experiments to validate this model, we believe this is the first attempt to conduct frequency-domain inverse modeling in vadose zone hydrology using soil moisture fluctuation.

On cost-efficient parallel iterative solvers for 3D frequency-domain seismic multisource viscoelastic anisotropic wave modeling

Solving large sparse linear systems in 3D frequency-domain seismic wave modeling, especially in viscoelastic anisotropic media, poses significant challenges due to the increasing number of discrete moduli and nonzero elements in the linear system matrix. The computational load surpasses that of acoustic or viscoacoustic media, making it even more challenging when dealing with multisource problems. Popular scientific tools for solving a linear system, such as multifrontal massively parallel sparse direct solver (MUMPS), structured matrix package (STRUMPACK), and portable extensible toolkit for scientific computation (PETSc), can be used, but their applicability to our specific problem has not been comprehensively evaluated. Our study aims to tackle the challenges in solving large, sparse, complex-valued symmetric linear systems with multiple right-hand side vectors for 3D frequency-domain seismic wave modeling. We have adopted the preconditioned conjugate gradient iterative algorithms as the foundation for our research, introducing two highly cost-effective parallel iterative solvers: the parallel symmetric successive overrelaxation conjugate gradient (P-SSORCG) and the parallel incomplete Cholesky conjugate gradient (P-ICCG). These novel solvers are subjected to a comprehensive comparative analysis against well-established scientific tools, such as MUMPS, STRUMPACK, and PETSc, in the context of 3D frequency-domain seismic wave modeling. We show their promising performances in a practical 3D SEG/EAGE overthrust model and demonstrate that the grouped P-SSORCG offers an efficient alternative to parallel direct solvers, particularly in situations wherein computational resources are limited.

Neural Network Design for Impedance Modeling of Power Electronic Systems Based on Latent Features.

Data-driven approaches are promising to address the modeling issues of modern power electronics-based power systems, due to the black-box feature. Frequency-domain analysis has been applied to address the emerging small-signal oscillation issues caused by converter control interactions. However, the frequency-domain model of a power electronic system is linearized around a specific operating condition. It thus requires measurement or identification of frequency-domain models repeatedly at many operating points (OPs) due to the wide operation range of the power systems, which brings significant computation and data burden. This article addresses this challenge by developing a deep learning approach using multilayer feedforward neural networks (FNNs) to train the frequency-domain impedance model of power electronic systems that is continuous of OP. Distinguished from the prior neural network designs relying on trial-and-error and sufficient data size, this article proposes to design the FNN based on latent features of power electronic systems, i.e., the number of system poles and zeros. To further investigate the impacts of data quantity and quality, learning procedures from a small dataset are developed, and K-medoids clustering based on dynamic time warping is used to reveal insights into multivariable sensitivity, which helps improve the data quality. The proposed approaches for the FNN design and learning have been proven simple, effective, and optimal based on case studies on a power electronic converter, and future prospects in its industrial applications are also discussed.

Harmonic State-Space Modeling and Closed-Loop Control of Single-Stage High-Frequency Isolated DC–AC Converter

The port harmonic features of the single-phase single-stage high-frequency isolated dc-ac converter is not analyzed so far and the corresponding theoretical basis for improving the current quality is still a research gap. In this paper, a linear model in frequency domain of the single-stage high-frequency isolated dc-ac converter is originally derived based on the combined harmonic state space and extended description function modeling technique. The systematic modeling process is analyzed and the accuracy of the modeling is verified by the simulation results. Combined with the model analysis, the harmonic coupling characteristics between the ac side and the dc side are clearly presented. On this basis, this paper proposes a closed-loop control strategy to reduce the decrease of the dc-side and ac-side current quality caused by the harmonic coupling at the control level. Furthermore, this paper constructs the compound controllers based on the P-type iterative learning to suppress the harmonic currents of the dc side and the ac side, respectively. The composite controller does not distinguish the harmonic frequency. Hence, the proposed controller achieves the effective suppression of the harmonic currents in real time. The effectiveness and feasibility of the proposed control strategy are verified by the experiments.

Optimal transonic buffet aerodynamic noise PSD predictions with Random Forest: Modeling methods and feature selection

To address challenges such as long computational cycles and high experimental measurement costs in obtaining Power Spectral Density (PSD) of aerodynamic noise, this study aims to enable a rapid assessment of buffet frequency and aerodynamic noise levels. The paper conducts a comparative analysis of the impact of different modeling methods and input features on prediction accuracy, proposing the time domain model, the full frequency domain model, and the single frequency model. The research reveals that the frequency domain model has an advantage over the time domain model in predicting aerodynamic noise, emphasizing the importance of selecting appropriate modeling methods. Additionally, based on whether frequency information is used as input features, the study introduces the full frequency domain model and the single frequency model. Results indicate that the single frequency model can significantly reduce the maximum relative error and Root Mean Square Error of the full frequency domain model by approximately three orders of magnitude, lowering the reconstruction error of the Proper Orthogonal Decomposition method by 2–3 orders of magnitude. Furthermore, this model demonstrates generalization across Mach numbers, angles of attack, and spatial positions, ensuring that the maximum absolute error of discrete peak frequencies is controlled within 1 Hz, and the relative error of discrete narrowband peaks is maintained at around 1 %.

Modelling stochastic and quasi-periodic behaviour in stellar time-series: Gaussian process regression versus power-spectrum fitting

ABSTRACT As the hunt for an Earth-like exoplanets has intensified in recent years, so has the effort to characterize and model the stellar signals that can hide or mimic small planetary signals. Stellar variability arises from a number of sources, including granulation, supergranulation, oscillations, and activity, all of which result in quasi-periodic or stochastic behaviour in photometric and/or radial velocity observations. Traditionally, the characterization of these signals has mostly been done in the frequency domain. However, the recent development of scalable Gaussian process regression methods makes direct time-domain modelling of stochastic processes a feasible and arguably preferable alternative, obviating the need to estimate the power spectral density of the data before modelling it. In this paper, we compare the two approaches using a series of experiments on simulated data. We show that frequency-domain modelling can lead to inaccurate results, especially when the time-sampling is irregular. By contrast, Gaussian process regression results are often more precise, and systematically more accurate, in both the regular and irregular time-sampling regimes. While this work was motivated by the analysis of radial velocity and photometry observations of main-sequence stars in the context of planet searches, we note that our results may also have applications for the study of other types of astrophysical variability such as quasi-periodic oscillations in X-ray binaries and active galactic nuclei variability.

QuadWave1D: An optimized quadratic formulation for spectral prediction of coastal waves

Spectral information of coastal waves and the associated statistical parameters (e.g., the significant wave height and mean wave period) over large spatial scales is essential for many applications (e.g., coastal safety assessments, coastal management and developments, etc.). This demand explains the necessity for accurate yet effective models. A well-known efficient modelling approach is the quadratic approach (often referred to as frequency-domain models, weakly nonlinear mild-slope models, amplitude models, etc.). The efficiency of this approach is achieved through modelling reduction of the original governing equations (e.g., Euler equations). Most significantly, wave nonlinearity is described solely by a single quadratic mode-coupling term. Therefore, doubts arise with regard to the predictive capabilities of the quadratic approach to reliably describe the nonlinear development of waves in the coastal environment where nonlinearity is typically significant. This study attempts to push the limit of the prediction capabilities of nonlinear coastal waves based on the quadratic approach. To this end, an optimization process is proposed, striving to extract the quadratic formulation which describes most adequately nonlinear wave developments over water depths and bathymetrical structures which characterize the coastal environment. The outcome is the model QuadWave1D: a fully dispersive quadratic model for coastal wave prediction in one-dimension. Based on a wide set of examples (including monochromatic, bichromatic and irregular wave conditions) and comparing to other representative quadratic formulations, it is found that QuadWave1D presents superior predictive capabilities of both the sea-swell components and the infragravity field.

High-Resolution Frequency-Domain Spectroscopic and Modeling Studies of Photosystem I (PSI), PSI Mutants and PSI Supercomplexes.

Photosystem I (PSI) is one of the two main pigment-protein complexes where the primary steps of oxygenic photosynthesis take place. This review describes low-temperature frequency-domain experiments (absorption, emission, circular dichroism, resonant and non-resonant hole-burned spectra) and modeling efforts reported for PSI in recent years. In particular, we focus on the spectral hole-burning studies, which are not as common in photosynthesis research as the time-domain spectroscopies. Experimental and modeling data obtained for trimeric cyanobacterial Photosystem I (PSI3), PSI3 mutants, and PSI3-IsiA18 supercomplexes are analyzed to provide a more comprehensive understanding of their excitonic structure and excitation energy transfer (EET) processes. Detailed information on the excitonic structure of photosynthetic complexes is essential to determine the structure-function relationship. We will focus on the so-called "red antenna states" of cyanobacterial PSI, as these states play an important role in photochemical processes and EET pathways. The high-resolution data and modeling studies presented here provide additional information on the energetics of the lowest energy states and their chlorophyll (Chl) compositions, as well as the EET pathways and how they are altered by mutations. We present evidence that the low-energy traps observed in PSI are excitonically coupled states with significant charge-transfer (CT) character. The analysis presented for various optical spectra of PSI3 and PSI3-IsiA18 supercomplexes allowed us to make inferences about EET from the IsiA18 ring to the PSI3 core and demonstrate that the number of entry points varies between sample preparations studied by different groups. In our most recent samples, there most likely are three entry points for EET from the IsiA18 ring per the PSI core monomer, with two of these entry points likely being located next to each other. Therefore, there are nine entry points from the IsiA18 ring to the PSI3 trimer. We anticipate that the data discussed below will stimulate further research in this area, providing even more insight into the structure-based models of these important cyanobacterial photosystems.

3D numerical simulation of frequency-domain elastic wave equation with a compact second-order scheme

Finite-difference frequency-domain (FDFD) modeling has gained popularity in recent years. However, its main drawback lies in the need to solve large sparse linear systems, which is computationally expensive, especially for 3D elastic wave simulations. The existing elastic wave optimal schemes improve the simulation accuracy at the cost of using large-sized stencils or high-order finite-difference (FD) operators, and most of them only consider equal grid spacing and solid media. To address these issues, we have proposed a compact second-order scheme for simulating 3D elastic wave propagation. Starting from the second-order FD discretization of the first-order velocity-stress expression, the compact discrete scheme of the second-order elastic wave equation is obtained by using a parsimonious staggered-grid strategy to eliminate the stress variables. In this way, the scheme preserves the ability to handle high-contrast velocity and liquid-solid media, and has a more compact and sparse impedance matrix than existing schemes, which helps save computational costs. We also use an antilumped mass strategy to further improve the modeling accuracy. Dispersion analysis indicates that our compact second-order scheme has better accuracy than the classic second-order scheme, and even better accuracy than the average derivative 27-point scheme at large Poisson's ratio. Compared with the existing 3D elastic wave schemes, the compact second-order scheme has advantages in computational cost for the same grid. Finally, we employ these schemes to implement 3D numerical simulations, validating the effectiveness of our proposed scheme.

The impact of modulational instability on coastal wave forecasting using quadratic models

Coastal wave forecasting over large spatial scales is essential for many applications (e.g., coastal safety assessments, coastal management and developments, etc.). This demand explains the necessity for accurate yet effective models. A well-known efficient modelling approach is the quadratic approach (often referred to as frequency-domain models, nonlinear mild-slope models, amplitude models, etc.). The efficiency of this approach stems from a significant modelling reduction of the original governing equations (e.g., Euler equations). Most significantly, the description of wave nonlinearity essentially collapses into a single mode coupling term determined by the quadratic interaction coefficients. As a result, it is expected that the efficiency achieved by the quadratic approach is accompanied by a decrease in prediction accuracy. In order to gain further insight into the predictive capabilities of this modelling approach, this study examines six different quadratic formulations, three of which are of the Boussinesq type and the other three are referred to as fully dispersive. It is found that while the Boussinesq formulations reliably predict the evolution of coastal waves, the predictions by the fully dispersive formulations tend to be affected by false developments of modulational instability. Consequently, the predicted wave fields by the fully dispersive formulations are characterized by unexpectedly strong modulations of the sea-swell part and associated unexpected infragravity response. The impact of the modulational instability on wave prediction based on the quadratic approach is further demonstrated using existing laboratory results of bichromatic and irregular wave conditions.

An open-source project for wind instrument modeling using digital waveguides

Digital waveguide methods for time-domain modeling of acoustic structures comprised of interconnected piece-wise one-dimensional cylinders, cones and toneholes have been well reported in the past. In this work, an open-source Matlab class is presented that can be used to model arbitrary wind instrument air column structures, defined by length, radii and hole geometric parameters, using digital waveguide methods. Fractional-delay filtering can be enabled or disabled, with support for both Thiran and Lagrange filter types of specified order. Thermoviscous losses can be modeling using either a discrete-time least squares or a shelf-filter fit, both of arbitrary order. Three different tonehole model options are provided (two-port, three-port or wave digital filter). End boundary conditions include closed, anechoic, ideally open, open flanged and open unflanged. The class object can be used either in single-sample iterative contexts (for example, with an attached excitation model) or with arbitrarily-sized input signals (for example, to compute a reflection function or impedance). The modeled geometry can be constructed manually by iteratively adding segments or holes, or a complete geometry can be specified in a file. This project is bundled together with a parallel and previously reported open-source project for frequency-domain transfer matrix modeling of air columns (https://github.com/garyscavone/acmt).

Automated design flow for synthesizable ADPLL: From specification to GDS

We propose an automated design flow for an all-digital phase-locked loop (ADPLL) that selects and implements a PLL layout that satisfies user given input specifications using place-and-route (PnR) tools within 1.2 h. The all-digital architecture enables the use of a theory-based frequency domain model for predicting the output specifications once the oscillator performance is characterized. The cell-based digitally controlled oscillator (DCO) is modeled by extracting the PDK and cell specific constants that characterize the effective current to capacitance ratio from only 3 sets of SPICE simulations. The constants are then used to predict the analog performance with an analytical model, which shows an error rate less than 1.5 % for estimating frequency range and power consumption. The generator guides the user to a feasible set of specifications using the analytical model by providing the achievable range of the failed specification. As design examples, 8 generated PLL designs and their post-parasitic performances are compared to input specifications, including one measurement result from a fabricated chip in 65 nm CMOS process.

Dynamic Receptance Analysis Combined with Hybrid FE-SEA Method to Predict Structural Noise from Long-Span Cable-Stayed Bridge in Urban Rail Transit

In this study, dynamic receptance analysis (DRA) is proposed and combined with hybrid finite element (FE)-statistical energy analysis (SEA) method to accurately predict structural noise from long-span cable-stayed bridge (LSCB) with steel box composite girder (SBCG) in urban rail transit (URT). To begin with, a vertical vehicle–track coupling model in frequency domain is established based on DRA, in which the rail is represented by an infinite Timoshenko beam supported by a series of fasteners that are regarded as springs with complex stiffness. The floating slab is regarded as the Euler beam with both ends free supported by steel springs. Using this model, the spectrums of the wheel–rail force and the forces transferred to the bridge can be efficiently obtained by taking rail roughness as the excitation. Due to the low modal density of the concrete deck, the hybrid FE-SEA method is introduced to establish the noise prediction model, in which the discontinuity caused by using distinct models for different frequency bands is avoided. Then the on-site noise tests of a LSCB with SBCG in URT are carried out to verify of the proposed method. Finally, based on the prediction method, the acoustic contributions of the bridge components are analyzed in detail. The force transfer characteristics as well as the noise reduction effects of different track structures are thoroughly investigated, so as to provide reference for the future research on bridge-borne noise control.

A Method to Compute Frequency Domain Models Based on Direction-Dependent Derivative of the Variation of Voltage and Current Phasors

Harmonic pollution and other potential problems are increasing due to the rising demand for Power Electronic devices in low-voltage distribution systems. The adequate modeling of the harmonic characteristics of these devices is essential for assessing their impact. Frequency Domain Models (FDMs) are based on either matrix or tensor definitions, and different methods have been proposed to compute those models' parameters. This paper proposes a method to compute matrix or tensor-based FDMs by exploiting the nonholomorphic properties of complex functions. Thus, the direction-dependent derivative of the variation of voltage-current phasors is optimized over measurements set. By proving that tensor and matrix-based models are equivalent, it is guaranteed that the method can be applied to compute both models. The Proposed and Tensorial Parametrization methods are compared using the power of the error signal as a percentage of the power of the current signal achieving a one-digit reduction in a proportion of 4:1.

Probabilistic Model-Based Reinforcement Learning Unmanned Surface Vehicles Using Local Update Sparse Spectrum Approximation

This article focuses on the computational efficiency of probabilistic model-based reinforcement learning (MBRL) in unmanned surface vehicles (USV) under unforeseeable and unobservable external disturbances. A novel MBRL approach, local update spectrum probabilistic model predictive control (LUSPMPC) is proposed to fully release the superiority of the probabilistic model approximated in the frequency domain in computational efficiency while mitigating its risk of overfitting during the learning procedure. It employs a local update strategy to relieve the violation of Bochner's theory, and a frequency clipping trick to encourage the approximated model to focus on the features in the low-frequency domain. Evaluated by the position-keeping task in a real USV data-driven simulation, LUSPMPC shows its significant advantages in computational efficiency while achieving better learning capability, generalization capability and control performances in a wide range of sparse scales compared with the baseline MBRL approaches that approximate their models in sample space and frequency domain, and therefore becomes an appealing solution for MBRL USV system defending against rapidly changing ocean disturbances.

Dispersive Optical Wireless Indoor Channels—From Frequency-Domain Modeling to Bit-Error-Rate Prediction

Dispersive Optical Wireless Indoor Channels—From Frequency-Domain Modeling to Bit-Error-Rate Prediction

First frequency-domain phenomenological model of the multipole asymmetry in gravitational-wave signals from binary-black-hole coalescence

Gravitational-wave signals from binaries that contain spinning black holes in general include an asymmetry between the +m and −m multipoles that is not included in most signal models used in LIGO-Virgo-KAGRA analysis to date. This asymmetry manifests itself in out-of-plane recoil of the final black hole and its inclusion in signal models is necessary both to measure this recoil, but also to accurately measure the full spin information of each black hole. We present the first model of the antisymmetric contribution to the dominant coprecessing-frame signal multipole throughout inspiral, merger, and ringdown. We model the antisymmetric contribution in the frequency domain, and take advantage of the approximations that the antisymmetric amplitude can be modeled as a ratio of the (already modeled) symmetric amplitude, and analytic relationships between the symmetric and antisymmetric phases during the inspiral and ringdown. The model is tuned to single-spin numerical-relativity simulations up to mass-ratio 8 and spin magnitudes of 0.8, and has been implemented in a recent phenomenological model for use in the fourth LIGO-Virgo-KAGRA observing run. However, the procedure described here can be easily applied to other time- or frequency-domain models. Published by the American Physical Society 2024