Frequency-domain Waveform Research Articles

Sound speed imaging of cortical bone and soft tissue based on frequency-domain ultrasound waveform tomography

Abstract As one of the ultrasound computed tomography (UCT) algorithms, full-waveform inversion (FWI) can recover clear and detailed internal structures of bones by iteratively minimizing the misfit between observed and numerical data. However, time domain full-waveform inversion (TDFWI) often lacks sufficient low-frequency information, and the computation of full-time data imposes a significant computational burden. Besides, there are few studies on whole-medium reconstruction that jointly invert the bone and surrounding soft tissues. In this study, an FWI-based frequency-domain UCT (FD-UCT) is utilized for simultaneously imaging the sound speed of bones and soft tissues, which facilitates the inversion efficiency while ensuring the existence of low-frequency information. Simulated studies show that the FD-UCT can both reconstruct bones with large acoustic impedance and distinguish subtle impedance differences within soft tissues to reveal lesions.

2-D Slicewise Waveform Inversion of Sound Speed and Acoustic Attenuation for Ring Array Ultrasound Tomography Based on a Block LU Solver.

Ultrasound tomography is an emerging imaging modality that uses the transmission of ultrasound through tissue to reconstruct images of its mechanical properties. Initially, ray-based methods were used to reconstruct these images, but their inability to account for diffraction often resulted in poor resolution. Waveform inversion overcame this limitation, providing high-resolution images of the tissue. Most clinical implementations, often directed at breast cancer imaging, currently rely on a frequency-domain waveform inversion to reduce computation time. For ring arrays, ray tomography was long considered a necessary step prior to waveform inversion in order to avoid cycle skipping. However, in this paper, we demonstrate that frequency-domain waveform inversion can reliably reconstruct high-resolution images of sound speed and attenuation without relying on ray tomography to provide an initial model. We provide a detailed description of our frequency-domain waveform inversion algorithm with open-source code and data that we make publicly available.

Gravitational radiation from eccentric binary black hole system in dynamical Chern-Simons gravity

Dynamical Chern-Simons (DCS) gravity, a typical parity-violating gravitational theory, modifies both the generation and propagation of gravitational waves from general relativity (GR). In this work, we derive the gravitational waveform radiated from a binary slowly-rotating black hole system with eccentric orbits under the spin-aligned assumption in the DCS theory. Compared with GR, DCS modification enters the second-order post-Newtonian (2PN) approximation, affecting the spin-spin coupling and monopole-quadrupole coupling of binary motion. This modification produces an extra precession rate of periastron. This effect modulates the scalar and gravitational waveform through a quite low frequency. Additionally, the dissipation of conserved quantities results in the secular evolution of the semimajor axis and the eccentricity of binary orbits. Finally, the frequency-domain waveform is given in the post-circular scheme, requiring the initial eccentricity to be ≲ 0.3. This ready-to-use template will benefit the signal searches and improve the future constraint on DCS theory.

Risk prediction of pulse wave for hypertensive target organ damage based on frequency-domain feature map

The application of deep learning to the classification of pulse waves in Traditional Chinese Medicine (TCM) related to hypertensive target organ damage (TOD) is hindered by challenges such as low classification accuracy and inadequate generalization performance. To address these challenges, we introduce a lightweight transfer learning model named MobileNetV2SCP. This model transforms time-domain pulse waves into 36-dimensional frequency-domain waveform feature maps and establishes a dedicated pre-training network based on these maps to enhance the learning capability for small samples. To improve global feature correlation, we incorporate a novel fusion attention mechanism (SAS) into the inverted residual structure, along with the utilization of 3 × 3 convolutional layers and BatchNorm layers to mitigate model overfitting. The proposed model is evaluated using cross-validation results from 805 cases of pulse waves associated with hypertensive TOD. The assessment metrics, including Accuracy (92.74 %), F1-score (91.47 %), and Area Under Curve (AUC) (97.12 %), demonstrate superior classification accuracy and generalization performance compared to various state-of-the-art models. Furthermore, this study investigates the correlations between time-domain and frequency-domain features in pulse waves and their classification in hypertensive TOD. It analyzes key factors influencing pulse wave classification, providing valuable insights for the clinical diagnosis of TOD.

Audio Scanning Network: Bridging Time and Frequency Domains for Audio Classification

With the rapid growth of audio data, there's a pressing need for automatic audio classification. As a type of time-series data, audio exhibits waveform fluctuations in both the time and frequency domains that evolve over time, with similar instances sharing consistent patterns. This study introduces the Audio Scanning Network (ASNet), designed to leverage abundant information for achieving stable and effective audio classification. ASNet captures real-time changes in audio waveforms across both time and frequency domains through reservoir computing, supported by Reservoir Kernel Canonical Correlation Analysis (RKCCA) to explore correlations between time-domain and frequency-domain waveform fluctuations. This innovative approach empowers ASNet to comprehensively capture the changes and inherent correlations within the audio waveform, and without the need for time-consuming iterative training. Instead of converting audio into spectrograms, ASNet directly utilizes audio feature sequences to uncover associations between time and frequency fluctuations. Experiments on environmental sound and music genre classification tasks demonstrate ASNet's comparable performance to state-of-the-art methods.

Fast and Fourier: extreme mass ratio inspiral waveforms in the frequency domain

Extreme Mass Ratio Inspirals (EMRIs) are one of the key sources for future space-based gravitational wave interferometers. Measurements of EMRI gravitational waves are expected to determine the characteristics of their sources with sub-percent precision. However, their waveform generation is challenging due to the long duration of the signal and the high harmonic content. Here, we present the first ready-to-use Schwarzschild eccentric EMRI waveform implementation in the frequency domain for use with either graphics processing units (GPUs) or central processing units (CPUs). We present the overall waveform implementation and test the accuracy and performance of the frequency domain waveforms against the time domain implementation. On GPUs, the frequency domain waveform takes in median 0.044 s to generate and is twice as fast to compute as its time domain counterpart when considering massive black hole masses ≥2×106M⊙ and initial eccentricities e0 > 0.2. On CPUs, the median waveform evaluation time is 5 s, and it is five times faster in the frequency domain than in the time domain. Using a sparser frequency array can further speed up the waveform generation, reaching up to 0.3 s. This enables us to perform, for the first time, EMRI parameter inference with fully relativistic waveforms on CPUs. Future EMRI models, which encompass wider source characteristics (particularly black hole spin and generic orbit geometries), will require significantly more harmonics. Frequency domain models will be essential analysis tools for these astrophysically realistic and important signals.

Inner product preconditioned trust-region methods for frequency-domain full waveform inversion

Full waveform inversion is a seismic imaging method which requires solving a large-scale minimization problem, typically through local optimization techniques. Most local optimization methods can basically be built up from two choices: the update direction and the strategy to control its length. In the context of full waveform inversion, this strategy is very often a line search. We here propose to use instead a trust-region method, in combination with non-standard inner products which act as preconditioners. More specifically, a line search and several trust-region variants of the steepest descent, the limited memory BFGS algorithm and the inexact Newton method are presented and compared. A strong emphasis is given to the inner product choice. For example, its link with preconditioning the update direction and its implication in the trust-region constraint are highlighted. A first numerical test is performed on a 2D synthetic model then a second configuration, containing two close reflectors, is studied. The latter configuration is known to be challenging because of multiple reflections. Based on these two case studies, the importance of an appropriate inner product choice is highlighted and the best trust-region method is selected and compared to the line search method. In particular we were able to demonstrate that using an appropriate inner product greatly improves the convergence of all the presented methods and that inexact Newton methods should be combined with trust-region methods to increase their convergence speed.

An Efficient Waveform Reconstruction Method for Digital Bandwidth Interleaving Sampling System

Digital bandwidth interleaving (DBI) technology is a method that can simultaneously improve the bandwidth and sampling rate of a sampling system. However, its waveform reconstruction algorithm is very complex, and the realization of real-time waveform reconstruction requires a great number of system parallel computing resources. This paper proposes a frequency-domain waveform reconstruction method for a DBI sampling system to improve the waveform reconstruction efficiency. This method completes digital mixing, filtering, and corrections in the frequency domain, and recovers the waveform from the discrete frequency domain information. This method takes advantage of the computational efficiency advantages of the frequency-domain filtering method compared to the time domain filtering. And it integrates multiple time-domain filter coefficients in the DBI system into a frequency response coefficient, so that one frequency-domain filtering is equivalent to multiple time-domain filtering operations. This paper also introduces a polyphase frequency-domain filtering structure, which has great advantages in computational complexity compared to the classical time-domain parallel polyphase filtering structure. To verify the effeciency of the method, an evaluation platform with 8 GHz bandwidth and 20 GSPS sampling rate is implemented to illustrate its performance. Both the classical time domain method and the proposed frequency domain method are verified in MATLAB and are compared for performance and resource consumption in FPGA. Experimental results show that the proposed method saves 10% look up tables (LUTs), 26% flip-flops(FFs), and 47% digital signal processing (DSP) slices compared to the classical time-domain method. Under the condition that the word length is less than 6 bits, the proposed method improves SFDR by more than 5 dB and SNR by more than 10 dB compared with the classical method.

Frequency-domain acoustic full waveform inversion with an embedded boundary method for irregular topography

In the implementation of full waveform inversion (FWI) to identify subsurface velocity distributions with land seismic data, which are often acquired in regions with irregular topography, wave equation-based modelling requires caution. In particular, when using the finite difference method (FDM), unwanted scattered waves are generated because irregular surfaces crossing a rectangular grid are discretized via a staircase approximation; hence, if the problems caused by this staircase approximation are disregarded, FDM-based FWI may fail due to the presence of undesirable wavefields. To resolve this problem, this study develops a 2D frequency-domain acoustic FWI technique using a 9-point FDM-based modelling scheme that includes an embedded boundary method (EBM). This study suggests a workflow for the whole EBM-based FWI process from the calculation of coefficients for the EBM-based 9-point FDM modelling to applying it to FWI for proper velocity updates. In numerical examples, using velocity models with a tilted surface and an arbitrarily fluctuating surface, we synthesize seismic data and verify the accuracy of EBM-based 9-point FDM modelling and its superiority over the conventional FDM by comparing it with wavefields derived from the spectral element method. Then, we show that our EBM-based FWI is able to estimate subsurface velocity distributions even though the model has irregular topography, which spoils the result of the conventional FWI.

Influence of Temporal and Spatial Fluctuations of the Shallow Sea Acoustic Field on Underwater Acoustic Communication.

In underwater acoustic communication (UAC) systems, the channel characteristics are mainly affected by spatiotemporal changes, which are specifically manifested by two factors: the effects of refraction and scattering caused by seawater layered media on the sound field and the random fluctuations from the sea floor and surface. Due to the time-varying and space-varying characteristics of a channel, the communication signals have significant variations in time and space. Furthermore, the signal shows frequency-selective fading in the frequency domain and signal waveform distortion in the time domain, which seriously affect the performance of a UAC system. Techniques such as error correction coding or space diversity are usually adopted by UAC systems to neutralize or eliminate the effects of deep fading and signal distortion, which results in a significant waste of limited communication resources. From the perspective of the sound field, this study used experimental data to analyze the spatiotemporal fluctuation characteristics of the signal and noise fields and then summarized the temporal and spatial variation rules. The influence of the system then guided the parameter configuration and network protocol optimization of the underwater acoustic communication system by reasonably selecting the communication signal parameters, such as frequency, bandwidth, equipment deployment depth, and horizontal distance.

Prediction of H-type Hypertension Based on Pulse Wave MFCC Features Using Mixed Attention Mechanism

PurposeH-type hypertension increases the risks of stroke and cardiovascular disease, posing a great threat to human health. Pulse diagnosis in traditional Chinese medicine (TCM) combined with deep learning can independently predict suspected H-type hypertension patients by analyzing their pulse physiological activities. However, the traditional time-domain feature extraction has a higher noise and baseline drift, affecting the classification accuracy. In this article, we propose an effective prediction on frequency-domain pulse wave features.MethodsFirst, we filter time-domain pulse waves via removal of high-frequency noises and baseline shift. Second, Hilbert–Huang Transform is explored to transform time-domain pulse wave into frequency-domain waveform characterized by Mel-frequency cepstral coefficients. Finally, an improved BiLSTM model, combined with mixed attention mechanism is built to be applied for prediction of H-type hypertension.ResultsWith 337 clinical cases from the Longhua Hospital affiliated to Shanghai University of TCM and Hospital of Integrated Traditional Chinese and Western Medicine, the threefold cross-validation results show that sensitivity, specificity, accuracy, F1-score and AUC reaches 93.48%, 95.27%, 97.48%, 90.77% and 0.9676, respectively. In addition, we calculate the feature importance both in time-domain and frequency-domain according to purity of nodes in Random Forest and study the correlation between features and classification.ConclusionThe proposed model achieves better generalization performance than the classical traditional ûmodels, and has a good reference value for TCM clinical auxiliary diagnosis.

New twists in compact binary waveform modeling: A fast time-domain model for precession

We present IMRPhenomTPHM, a phenomenological model for the gravitational wave signals emitted by the coalescence of quasi-circular precessing binary black holes systems. The model is based on the "twisting up" approximation, which maps non-precessing signals to precessing ones in terms of a time dependent rotation described by three Euler angles, and which has been utilized in several frequency domain waveform models that have become standard tools in gravitational wave data analysis. Our model is however constructed in the time domain, which allows several improvements over the frequency domain models: we do not use the stationary phase approximation, we employ a simple approximation for the precessing Euler angles for the ringdown signal, and we implement a new method for computing the Euler angles through the evolution of the spin dynamics of the system, which is more accurate and also computationally efficient.

Study on Optimization of Infrasound Filtering Method for Coal Sample Failure under Load

Effective filtering of the infrasound signal generated by coal samples is the basis for realizing the prediction of the infrasound of coal sample damage. Based on the infrasonic signal test of the coal samples during the loading process, a simulation method was used to construct a mixed signal containing noise signals and infrasound signals. Three methods are used to filter the mixed signal, including wavelet filtering, EMD filtering, and EMD-wavelet joint filtering. The filtering effect was compared by correlation coefficient, signal-to-noise ratio, and frequency domain waveform graph. The comparison results showed that the EMD-wavelet joint filtering method had the highest correlation coefficient and signal-to-noise ratio after noise filtering, and the noise signal in the frequency domain waveform diagram was the most thorough. It provides a new method for filtering infrasound signals in the process of coal sample loading, which is greatly significant for improving the accuracy of infrasound prediction of coal sample damage.

Terahertz Nondestructive Testing Method of Oil-paper Insulation Debonding and Foreign Matter Defects

Defects, such as debonding and foreign matters in transformer insulation paperboard, lead to local field strength concentration, thereby seriously affecting the safe operation of equipment. At present, industrial X-ray computed tomography scanning technology is mostly used to detect such defects. However, the equipment is expensive, the operation is complicated, and radiation hazard exists. In this study, terahertz time domain spectroscopy is introduced to explore the nondestructive testing method of oil-paper insulation defects. Three typical insulation paperboard defects of interface debonding, metal foreign matter mixing, and local carbonization traces were taken as the research objects. An artificial defect model is prepared. The time and frequency domain waveform characteristics of terahertz pulse wave propagating in the defect model are tested and analyzed. The results show that when the thickness of insulation paperboard covering is less than 5 mm, based on the amplitude and delay characteristics of terahertz time-domain signal, the location and size of typical internal defects can be accurately obtained, and time spectrum imaging can be realized. This study proves theoretically and experimentally the feasibility of noncontact and nondestructive testing for the internal defects of insulation paperboard by using terahertz technology.

Time–Frequency Domain Characteristics of Acoustic Emission Signals and Critical Fracture Precursor Signals in the Deep Granite Deformation Process

To study the crack evolution law and failure precursory characteristics of deep granite rocks in the process of deformation and failure under high confining pressure, granite samples obtained from a depth of 1150 m are tested using a TAW-2000 triaxial hydraulic servo testing machine and a PCI-II acoustic emission monitoring system. Based on the stress–strain curve and IET function, the loading process of the sample is divided into five stages: crack closure, linear elastic deformation, microcrack generation and development, macroscopic fracture generation and energy surge, and post-peak failure. The evolution trend and fracture evolution law of the acoustic emission signal event interval function in different stages are analyzed. In particular, the signals with an amplitude greater than 85 dB, a peak frequency greater than 350 kHz, and a frequency centroid greater than 275 kHz are defined as the failure precursor signals before the rock reaches the peak stress. The defined precursor signal conditions agree well with the experimental results. The time–frequency analysis and wavelet packet decomposition of the precursor signal are performed on the extracted characteristic signal of the failure precursor. The results show that the time-domain signal is in the form of a continuous waveform, and the frequency-domain waveform has multi-peak coexistence that is mainly concentrated in the high-frequency region. The energy distribution obtained by the wavelet packet decomposition of the characteristic signal is verified with the frequency-domain waveform. The energy distribution of the signal is mainly concentrated in the 343.75–375 kHz frequency band, followed by the 281.25–312.5 kHz frequency band. The energy proportion of the high-frequency signal increases with the confining pressure.

Frequency-domain reflection waveform inversion with generalized internal multiple imaging

Full-waveform inversion (FWI) has the potential to provide a high-resolution detailed model of the earth’s subsurface, but it often fails to do so if the starting model differs significantly from the true one. Reflection waveform inversion (RWI) is a popular method for building a sufficiently accurate initial model for FWI. In traditional RWI, the low-wavenumber updates are always computed and captured by smearing the data misfit along the reflection path with the help of migration/demigration. However, the success of RWI relies heavily on accurately reproducing the data in demigration. Thus, we have introduced a new generalized internal multiple imaging-based RWI (GIMI-RWI) implementation, in which we avoid the Born modeling and update the primary reflection kernel directly. In GIMI-RWI, we store one reflection kernel for each source-receiver pair, preserving the unique wavepath for every single source-receiver trace. Subsequently, the convolution between the data residuals and the corresponding reflection kernel can build the tomographic velocity updates. In this situation, the long-wavelength tomographic updates are free of migration footprints and will contribute a smoother background velocity to reduce the cycle-skipping risk and stabilize the followed FWI process. In addition, the GIMI-RWI method is source independent because it entirely relies on the data. Using a synthetic example extracted from the Sigsbee2A model, we find the reliable performance of the GIMI-RWI technique.

Key Technology Optimization and Development of New Energy Enterprises of Photovoltaic Power Generation

In order to improve the algorithm of time-varying parameters and unknownparameters adaptability, avoid assuming the approximate part deviationcaused by the algorithm, this paper proposes a adaptive control algorithm, thealgorithm based on lyapunov direct method to predict the output voltage inthe process of estimating each parameter in a reasonable manner to parameterestimation error with the actual output current and current automatic adjust-ment. The adaptive control of current tracking is realized and the error causedby assuming voltage or current and neglecting line resistance is avoided inthe predictive current control algorithm. The simulation results show thatthe tracking current can track the target current with high precision fromt = 0 in the presence of random noise, and the power factor is close to 1,showing a good steady-state performance. Frequency domain waveform, thecalculated harmonic distortion rate is 2.2418%, waveform quality is good andeach harmonic amplitude is small. Conclusion: adaptive control algorithmcan quickly and accurately realize current tracking and greatly suppress thenoise.

Towards the routine use of subdominant harmonics in gravitational-wave inference: Reanalysis of GW190412 with generation X waveform models

We re-analyse the gravitational-wave event GW190412 with state-of-the-art phenomenological waveform models. This event, which has been associated with a black hole merger, is interesting due to the significant contribution from subdominant harmonics. We use both frequency-domain and time-domain waveform models. The PhenomX waveform models constitute the fourth generation of frequency-domain phenomenological waveforms for black hole binary coalescence; they have more recently been complemented by the time-domain PhenomT models, which open up new strategies to model precession and eccentricity, and to perform tests of general relativity with the phenomenological waveforms approach. Both PhenomX and PhenomT have been constructed with similar techniques and accuracy goals, and due to their computational efficiency this "generation X" model family allows the routine use of subdominant spherical harmonics in Bayesian inference. We show the good agreement between these and other state-of-the-art waveform models for GW190412, and discuss the improvements over the previous generation of phenomenological waveform models. We also discuss practical aspects of Bayesian inference such as run convergence, variations of sampling parameters, and computational cost.

Research on Fault Extraction Method of CYCBD Based on Seagull Optimization Algorithm

Maximum cyclostationarity blind deconvolution (CYCBD) can recover the periodic impulses from mixed fault signals comprised by noise and periodic impulses. In recent years, blind deconvolution has been widely used in fault diagnosis. However, it requires a preset of filter length, and inappropriate filter length may cause the inaccurate extraction of fault signal. Therefore, in order to determine filter length adaptively, a method to optimize CYCBD by using the seagull optimization algorithm (SOA) is proposed in this paper. In this method, the ratio of SNR to kurtosis is used as the objective function; firstly, SOA is used to search the optimal filter length in CYCBD by iteration, and then it uses the optimal filter length to perform CYCBD; finally, the frequency‐domain waveform is determined through Fourier transformation. The method proposed is applied to the fault extraction of a simulated signal and a test vibration signal of the closed power flow gearbox test bed, and the fault frequency is successfully extracted, in addition, using maximum correlation kurtosis deconvolution (MCKD) and multipoint optimal minimum entropy deconvolution adjusted (MOMEDA) to compare with CYCBD‐SOA, which validated availability of the proposed method.

Three-dimensional frequency-domain full waveform inversion based on the nearly-analytic discrete method

The nearly analytic discrete (NAD) method is a kind of finite difference method with advantages of high accuracy and stability. Previous studies have investigated the NAD method for simulating wave propagation in the time-domain. This study applies the NAD method to solving three-dimensional (3D) acoustic wave equations in the frequency-domain. This forward modeling approach is then used as the “engine” for implementing 3D frequency-domain full waveform inversion (FWI). In the numerical modeling experiments, synthetic examples are first given to show the superiority of the NAD method in forward modeling compared with traditional finite difference methods. Synthetic 3D frequency-domain FWI experiments are then carried out to examine the effectiveness of the proposed methods. The inversion results show that the NAD method is more suitable than traditional methods, in terms of computational cost and stability, for 3D frequency-domain FWI, and represents an effective approach for inversion of subsurface model structures.