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  • Time Domain Analysis
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Articles published on time-domain

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  • Research Article
  • 10.1121/10.0043842
Theoretical analysis and verification of convergence for the overall modeling algorithm in narrowband active noise control.
  • May 1, 2026
  • The Journal of the Acoustical Society of America
  • Li Rao + 5 more

Online secondary path modeling is essential for the robust performance of adaptive active noise control (ANC) systems. The Overall Modeling Algorithm (OMA) simultaneously models both the primary and secondary paths during control filter adaptation, featuring a simple algorithm structure and no need for auxiliary noise. While previous studies have analyzed its convergence only in broadband ANC systems, the convergence behavior in narrowband ANC (NANC) systems remains unclear. Therefore, this paper analyzes the convergence of OMA in NANC systems in both the time and frequency domains. The results show that OMA-based NANC systems converge when the lengths of the modeled primary path, the modeled secondary path, and the control filter are each at least twice the number of noise frequencies. If the modeled path length equals the true path length, full-band convergence can be achieved when the number of noise frequencies is at least half of the path length. This indicates that complete secondary path information can be obtained using only a limited number of tonal signals. The theoretical analysis is validated through simulations and experiments under various NANC scenarios.

  • Research Article
  • Cite Count Icon 1
  • 10.1016/j.cmpb.2026.109264
Artificial intelligence approaches for non-invasive diabetes prediction using ECG signals: A systematic review.
  • May 1, 2026
  • Computer methods and programs in biomedicine
  • Kiruthika Balakrishnan + 6 more

Diabetes is a major global health challenge, with many individuals remaining undiagnosed due to the limitations of traditional screening methods. Artificial intelligence (AI)-based electrocardiogram (ECG) analysis offers a promising, non-invasive approach for the early detection of diabetes. This systematic review aims to critically evaluate machine learning (ML) and deep learning (DL) models developed for non-invasive prediction of diabetes and prediabetes using ECG signals. A comprehensive literature search was conducted across PubMed, Embase, Web of Science, IEEE Xplore, and ACM Digital Library in accordance with PRISMA 2020 guidelines. Twenty-five studies met the inclusion criteria. Extracted data included ECG input types, model architectures, preprocessing methods, feature sets, validation strategies, and performance metrics. Most studies used small, single-site, cross-sectional datasets, with sample sizes ranging from 24 to over 190,000 individuals. ECG preprocessing methods varied widely, including filtering, normalization, and decomposition. Features were extracted from time, frequency, morphological, and non-linear domains, though formal feature selection was applied inconsistently. ML and DL models reported high internal accuracy (>90%) but most lacked external validation and subgroup performance assessments. Notably, no study specifically focused on rural or underserved populations, and only one provided open-source code. AI-based ECG analysis demonstrates strong potential for detecting diabetes; however, current research is limited by generalizability issues, lack of standardized methods, poor external validation, and insufficient transparency. Future studies should prioritize rigorous validation, reproducibility, fairness audits, and applications in rural and underserved settings to ensure equitable and clinically viable deployment of these models.

  • Research Article
  • 10.1016/j.jcis.2026.140000
Photoluminescence of silicon nanorods via plasmonic gold nanopore arrays.
  • May 1, 2026
  • Journal of colloid and interface science
  • Yizhi Wu + 3 more

Photoluminescence of silicon nanorods via plasmonic gold nanopore arrays.

  • Research Article
  • 10.1016/j.egyai.2026.100704
A deep learning framework for heat demand forecasting using time–frequency representations of decomposed features
  • May 1, 2026
  • Energy and AI
  • Adithya Ramachandran + 5 more

A deep learning framework for heat demand forecasting using time–frequency representations of decomposed features

  • Research Article
  • 10.1016/j.oceaneng.2026.124761
Coupled hydroelastic responses of horizontal bending and torsion of a flexible large ship using a time domain method
  • May 1, 2026
  • Ocean Engineering
  • Vijith Pp + 1 more

Coupled hydroelastic responses of horizontal bending and torsion of a flexible large ship using a time domain method

  • Research Article
  • 10.1109/tpwrs.2025.3627296
An $H_\infty$-Optimization Reinforced Adaptive VSG Control to Improve the Overall Stability of a PV-Dominated Power System
  • May 1, 2026
  • IEEE Transactions on Power Systems
  • Deepak Kumar Soni + 1 more

The extensive integration of inertia-less renewable energy sources, such as solar photovoltaic (PV) systems, has introduced several stability challenges. The virtual synchronous generator (VSG) has emerged as a promising solution for addressing low-inertia issues. However, the integration of numerous VSG-controlled PV plants into the power system may introduce additional oscillations due to the dynamic interaction between VSG and PV inverter controls. In this paper, a large number of utility-scale VSG-controlled PV units are deployed to analyze their effect on the small-signal oscillations. Subsequently, an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula>-based VSG parameters optimization is proposed to enhance the small-signal stability. A systematic modal analysis procedure is also established to define the highest and lowest levels for adaptive variation of VSG parameters to further improve the large-signal stability. These optimized and adaptive features are combined in the form of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula>-optimization reinforced adaptive (HORA) VSG control to improve the overall stability of the PV-dominated grid. The performance of the proposed HORA VGS control is compared with non-adaptive and conventional adaptive VSG control techniques. The studies are conducted on the IEEE 68-bus, 16-machine power system by means of both frequency and time domain analyses through various case studies on the MATLAB/Simulink platform.

  • Research Article
  • 10.1088/1475-7516/2026/05/032
Spectral imaging with QUBIC: building frequency maps from Time-Ordered-Data using Bolometric Interferometry
  • May 1, 2026
  • Journal of Cosmology and Astroparticle Physics
  • M Regnier + 36 more

The search for relics from the inflation era in the form of B-mode polarization of the CMB is a major challenge in cosmology. The main obstacle appears to come from the complexity of Galactic foregrounds that need to be removed. Multi-frequencyobservations are key to mitigating their contamination and mapping primordial fluctuations. We present “Spectral-Imaging”, a method to reconstruct sub-frequency maps of the CMB polarization within the instrument's physical bandwidth, a unique feature of Bolometric Interferometry that could be crucial for foreground mitigation as it provides an increased spectral resolution. Our technique uses the frequency evolution of the shape of the Bolometric Interferometer's synthesized beam to reconstruct frequency information from the time domain data. We reconstruct sub-frequency maps using an inverse problem approach based on detailed modeling of the instrument acquisition. We use external data to regularize the convergence of the estimator and account for bandpass mismatch and varying angular resolution. The reconstructed maps are unbiased and allow exploiting the spectral-imaging capacity of QUBIC. Using end-to-end simulations of the QUBIC instrument, we perform a cross-spectra analysis to extract a forecast on the tensor-to-scalar ratio constraint of σ(r)= 0.0225 after component separation.

  • Research Article
  • 10.1016/j.oceaneng.2026.125061
A time domain method for the calculation of motions and wave loads of hovercraft in waves
  • May 1, 2026
  • Ocean Engineering
  • Zhihua Zuo + 4 more

A time domain method for the calculation of motions and wave loads of hovercraft in waves

  • Research Article
  • 10.1016/j.peh.2026.100417
The effect of sleep quantity and quality on exercise and academic performance, autonomic function, wellness and cognition in youth athletes
  • May 1, 2026
  • Performance Enhancement &amp; Health
  • Melissa Skein + 1 more

The aim was to examine the effect of sleep restriction, fragmentation, and extension on athletic and academic performance, cognition, autonomic function, and mood of youth athletes. Sixteen pre-elite youth athletes completed four sleep experimental trials in a randomised-control design. Each trial included sleep restriction to 4 h (RES), sleep fragmentation by periodic waking throughout the night (FRAG), sleep extension to 10 h (EXT), or control/normal night sleep (CONT). The following day, testing included resting heart rate variability (HRV); exercise tests, Stroop task, and mood and wellness questionnaires. Time domain HRV data indicate no differences between conditions (P = 0.126 – 0.945, d = 0.11 – 0.67), while frequency domain indices indicate resting very low frequency (VLF) % contribution higher in RES compared to CONT and RES (P = 0.05, d = 0.86 – 0.96). Stroop reaction times were slower and accuracy lower in FRAG (P = 0.001–0.009; d = 1.90 – 2.55), while maths results were not different between conditions (P = 0.91; d = 0.13 – 0.58). There were no differences between conditions for sprint times, agility times, and vertical jump height (P = 0.38–0.98; d = 0.02 – 0.35). Throwing reaction task accuracy was lower in FRAG compared to CONT and RES (P = 0.006–0.05; d = 0.8) with moderate to large effects noted for throwing duration ( d = 0.43 – 1.21). Scores for ‘positive’ feelings were lower (P = 0.02 - 0.001; d = 0.51 – 0.99) and ‘negative’ feelings were increased for RES and FRAG compared to CONT (P = 0.003–0.08; d = 1.01 – 1.84). Perceived wellness was lower for RES compared to CONT (P = 0.016 – 0.0001; d = 0.9 – 2.34). Sleep fragmentation and restriction had no significant effects on anaerobic exercise performance or academic tests, but significant decrements were evident in mood states, autonomic regulation, and accuracy during complex cognition tasks.

  • Research Article
  • 10.1021/acs.nanolett.6c01662
Three-Dimensional Nanopatterning Using Extreme Ultraviolet Colloidal Talbot Lithography.
  • Apr 30, 2026
  • Nano letters
  • Saurav Mohanty + 4 more

While extreme ultraviolet (EUV) lithography has enabled the continued scaling toward high-resolution features, existing processes are limited to patterning of planar two-dimensional (2D) structures. This work demonstrates EUV colloidal Talbot lithography (CTL) for the patterning of 3D nanostructures with 25 nm minimum feature sizes. In this approach, a monolayer of self-assembled nanospheres is utilized as a binary mask and illuminated using a tabletop high-harmonic generation (HHG) EUV source to form a volumetric intensity pattern for proximity-field printing. The interference pattern formation is investigated using finite difference time domain (FDTD) simulations and maintains an adequate fringe contrast within the volume. Experimental results demonstrate the fabrication of 2D nanostructures with tunable unit-cell geometry and 3D nanostructures down to 25 nm using a single exposure. This cost-effective approach enables single-exposure 3D EUV lithography with low hardware requirements and has broad applications in nanophotonics, quantum devices, and advanced materials.

  • Research Article
  • 10.1038/s41598-026-50621-z
Multi-view dynamic manifold reconstruction with adaptive cross-attention fusion enables noise-robust bearing fault diagnosis.
  • Apr 29, 2026
  • Scientific reports
  • Lei Yang + 3 more

To address the issues that bearing fault features are easily submerged under strong noise and that manifold topologies are prone to collapse, this paper proposes a Multi-view Dynamic Manifold Reconstruction and Adaptive Cross-Attention Fusion Network (MDM-CA Net). First, based on the theory of phase space reconstruction, dynamic K-nearest neighbor graphs are constructed in both the time domain and the frequency domain. A dual-channel graph convolutional network is employed to mine the intrinsic geometric structure of the signal, while complementary information from multiple views is utilized to filter out spurious connections induced by noise, thereby isolating noise outliers at the representation level. Second, a noise-aware temporal enhancement module centered on a bidirectional gated recurrent unit and integrated with a global attention mechanism is developed to adaptively suppress background noise interference. Finally, a Transformer-style cross-attention strategy is introduced, where temporal features serve as queries to retrieve critical patterns from spatial topologies, enabling deep semantic alignment and nonlinear interaction between heterogeneous spatiotemporal features. Experimental results on three public datasets, CWRU, SEU, and PU, demonstrate that MDM-CA Net achieves optimal comprehensive performance under both same-domain and cross-domain operating conditions. Under the extreme condition with a signal-to-noise ratio as low as - 4 dB, it still maintains diagnostic accuracies of 94.2%, 93.5%, and 95.8%, respectively. Ablation studies confirm the synergistic enhancement effect among the modules: the multi-view mechanism drives high precision, while cross-attention drives high recall, and their collaboration achieves an optimal balance.

  • Research Article
  • 10.1364/ao.580602
Small leak detection of gas pipelines with Φ-OTDR using an improved MobileNetV3-BiLSTM network
  • Apr 28, 2026
  • Applied Optics
  • Jun Li + 6 more

This paper presents a lightweight deep learning approach for detecting small leaks in buried gas pipelines using a phase-sensitive optical time domain reflectometry (Φ-OTDR) system. Vibration signals acquired from a distributed optical fiber vibration sensor (DOFVS) are converted into time–frequency images via continuous wavelet transform (CWT) to facilitate joint spatiotemporal feature extraction. An improved model that integrates a lightweight MobileNetV3 backbone with a bidirectional LSTM (BiLSTM) module is proposed to capture both spatial patterns from individual CWT images and temporal dependencies across consecutive frames. Experimental results demonstrate an overall accuracy of 95.96% in classifying four leak pressure levels, including the reliable detection of leaks as small as 1/16 inch under pressures as low as 0.1 MPa. Compared to conventional CNN models, an improved recognition accuracy of 8%–12% is demonstrated for the identification of low-pressure and small-aperture leakage conditions.

  • Research Article
  • 10.1038/s41440-026-02650-4
Role of characteristic impedance in carotid stiffness and cognitive dysfunction: interaction with proximal aortic stiffness.
  • Apr 27, 2026
  • Hypertension research : official journal of the Japanese Society of Hypertension
  • Chao-Feng Liao + 3 more

Increased stiffness in the proximal aorta and carotid artery, both crucial for regulating blood pressure and flow pulsatility, may contribute to cerebral microcirculation damage and cognitive decline. While aortic stiffness measured by aortic characteristic impedance (Zc) has been linked to suspected mild cognitive impairment (MCI), the role of carotid stiffness remains unclear due to inconsistent findings using traditional distensibility measures. This study investigates the relationship between carotid characteristic impedance (CCI) and suspected MCI, and examines how CCI interacts with Zc in contributing to cognitive dysfunction. A total of 1423 healthy community residents (average age 59.8 ± 11.7 years; 46.9% male) underwent comprehensive hemodynamic evaluations and carotid ultrasonography. CCI and Zc were calculated in the time domain, and the characteristic impedance ratio (CIR), defined as CCI/Zc, was used to assess the influence of impedance mismatch. Suspected MCI was determined using education-adjusted Mini-Mental State Examination (MMSE) cut-offs. Among participants, 478 (33.6%) were identified with suspected MCI. These individuals showed significantly higher CCI, while other carotid distensibility parameters were not significantly different. CCI was the only carotid stiffness measure independently associated with suspected MCI (OR per SD: 1.18; 95% CI: 1.02-1.36). CIR was negatively associated with MCI (OR: 0.84; 95% CI: 0.73-0.95), suggesting that a mismatch in impedance contributes to cognitive decline. The combination of elevated Zc and CCI was the strongest predictor of suspected MCI (OR: 2.10; 95% CI: 1.47-2.98). These findings underscore CCI as a sensitive and valuable marker for assessing carotid stiffness in relation to cognitive dysfunction.

  • Research Article
  • 10.3390/s26092698
Radar Resolution Enhancement Based on Burg-Aided MIMO-DBS and Burg-Aided MIMO-SAR \u2020
  • Apr 27, 2026
  • Sensors (Basel, Switzerland)
  • Muge Bekar + 4 more

Autonomous systems require sensors that provide high-resolution imagery in adverse lighting and weather conditions for advanced situational awareness. In this regard, radars are a mandatory component of autonomous systems. Although Multiple-Input Multiple-Output (MIMO) radars provide high angular resolution beyond that of their actual physical dimension, much higher cross-range resolutions are required, especially in traffic congested areas, to differentiate and recognize closely positioned targets. The motion of the MIMO radar platform can be exploited to obtain higher cross-range resolution in the off-boresight direction, using Synthetic Aperture Radar (SAR) and Doppler Beam Sharpening (DBS) techniques, but improvements in the boresight direction, the most crucial direction for path planning, require the use of super-resolution techniques. This paper proposes a technique that combines the Burg algorithm with MIMO-SAR and MIMO-DBS radar data to enhance the cross-range resolution in the boresight direction and to achieve further enhanced cross-range resolution in off-boresight directions. The proposed technique is applied to both frequency domain and time domain data in back-projection (BP) and DBS image formation processing. A comprehensive comparison is made, with evaluation of corresponding performance and operational complexity. The performance of the technique is validated through simulation, lab-based and real-world experiments at a frequency of 77 GHz.

  • Research Article
  • 10.1088/2057-1976/ae607c
Optimized VCG signal compression using sparse PSO
  • Apr 27, 2026
  • Biomedical Physics & Engineering Express
  • Aditya Tiwari + 2 more

Vectorcardiogram (VCG) signal compression is very much in demand in the present-day scenario due to the increasing number of cardiac patients. Hence, in this paper, a new technique is proposed that compresses VCG signal by optimizing the tunable quality wavelet transform (TQWT) parameters. The noise in VCG signal is firstly removed by applying a Savitzky-Golay filter, and then passing noise-free signal to an optimization algorithm that optimizes the TQWT parameters, and obtains the frequency domain signal. This signal is then quantized through dead-zone quantization and processed by a lossless compression mechanism: run-length encoding (RLE) to improve the compression ratio & encode the signal. This compressed signal is reconstructed by Inverse RLE to obtain the decoded signal. Inverse of TQWT is applied to get the reconstructed signal back from the transformed frequency domain to time domain. The parameters of TQWT, especially theQandR, are optimized to get the highestCRat lowest percent root-mean-square-difference(PRD)with best reconstruction quality and least distortions, along with acceptable values of signal-to-noise-ratio(SNR), quality score(QS), andSimilaritywith lowest mean-square-error(MSE). The comparative analysis of different optimization methods indicates that the sparse-particle swarm optimization is best among all the approaches for the tuning of parameters in TQWT for VCG signal compression and reconstruction achieving aCRof 48.18 at aPRDof 3.68,SNRof 29.39,QSof 15.71, similarity of 0.99845,MSEof 0.00016, withQvalue of 2.04307 andRvalue of 1.20568 withcomputational timeof 4.48508 s.

  • Research Article
  • 10.1142/s0219876226500271
Implementing and Programming Meshfree Collocation with Fast Moving Least-Squares Reproducing Kernel for Elastostatics and Elastodynamics
  • Apr 25, 2026
  • International Journal of Computational Methods
  • Dhafer K Jadaan + 3 more

In this paper, meshfree collocation with fast-moving least-squares reproducing kernel was implemented to write down and execute numerical solutions for some applications in elastostatics and elastodynamics. The spatial discretization using meshfree collocation method was carried out on the equilibrium differential equations of elastostatics and elastodynamics and the corresponding boundary conditions. The resulting discrete forms were solved for benchmark problems in the one- and two-dimensional cases. In each case, a convergence study was conducted to ascertain the utility and efficacy of the developed solutions. For elastodynamics, the time domain, however, was discretized using the Newmark beta time-integration scheme. The latter combination was implemented to solve suitable benchmark problems in the one-dimensional and two-dimensional cases. In each case, a stability study was conducted to demonstrate, again, the method’s efficacy in handling elastodynamic problems.

  • Research Article
  • 10.1038/s41524-026-02088-9
Enhancing the efficiency of time-dependent density functional theory calculations of dynamic response properties.
  • Apr 25, 2026
  • npj computational materials
  • Zhandos A Moldabekov + 6 more

X-ray Thomson scattering (XRTS) constitutes an essential technique for diagnosing material properties under extreme conditions, such as high pressures and intense laser heating. Time-dependent density functional theory (TDDFT) is one of the most accurate available ab initio methods for modeling XRTS spectra, as well as a host of other dynamic material properties. However, strong thermal excitations, along with the need to account for variations in temperature and density as well as the finite size of the detector significantly increase the computational cost of TDDFT simulations compared to ambient conditions. In this work, we present a broadly applicable method for optimizing and enhancing the efficiency of TDDFT calculations. Our approach is based on a one-to-one mapping between the dynamic structure factor and the imaginary time density-density correlation function, which naturally emerges in Feynman's path integral formulation of quantum many-body theory. Specifically, we combine rigorous convergence tests in the imaginary time domain with a constraints-based attenuation of narrow-band fluctuations to improve the efficiency of TDDFT modeling without the introduction of any significant bias. As a result, we can report a speed-up by up to an order of magnitude, thus substantially reducing the burden of computational cost required for XRTS analysis.

  • Research Article
  • 10.1177/14759217261442130
Weighted bi-domain sparse decomposition for encoder-signal-based planetary gearbox fault diagnosis
  • Apr 24, 2026
  • Structural Health Monitoring
  • Baoxiang Wang + 5 more

As key transmission components in mechanical systems, gearboxes often operate under harsh environments and heavy-load conditions, making them susceptible to various types of damage. In recent years, built-in encoder signals have attracted increasing attention for rotating machinery health monitoring due to their low cost, ease of acquisition, and direct correlation with rotational motion. However, fault-related features in encoder signals are usually weak and easily submerged by strong harmonic interference and noise, posing significant challenges for accurate fault identification and feature extraction. To address this issue, this article proposes a weighted bi-domain sparse decomposition (WBSD) model for encoder signal analysis and fault diagnosis of gearboxes. The proposed WBSD model exploits the distinct morphological characteristics of fault-induced impulses and interference components in both the time and frequency domains. Specifically, two dedicated nonconvex regularization terms are constructed to enforce periodic group sparsity of fault impulses in the time domain and spectral sparsity of harmonic interference in the frequency domain by introducing weighted coefficients, periodic binary vectors, and nonconvex penalty functions, thereby enabling accurate separation and sparse representation of fault features. Furthermore, an efficient iterative solving algorithm is developed for the WBSD model by integrating the alternating direction method of multipliers with the majorization–minimization method. Experimental results obtained from both simulated signals and real encoder signals collected from a planetary gearbox test platform demonstrate that the proposed WBSD model consistently outperforms comparative methods in extracting weak fault impulses under strong noise and interference, confirming its effectiveness and practical applicability for fault diagnosis of gearboxes.

  • Research Article
  • 10.1002/vnl.70115
Enhancing Damping in MEX ‐Fabricated ABS With Carbon Black: Free‐Decay Analysis, Estimator Fusion, and Mechanical Trade‐Offs
  • Apr 24, 2026
  • Journal of Vinyl and Additive Technology
  • Sabri Can Ekerer + 3 more

ABSTRACT Acrylonitrile–butadiene–styrene (ABS) cantilever beams were reinforced with carbon black (CB) at 0–2 wt% and fabricated by mechanical extrusion (MEX)‐based additive manufacturing to improve vibration damping without compromising strength. Free‐decay responses were processed with three complementary estimators—logarithmic decrement (time domain), half‐power bandwidth (frequency domain), and an envelope‐fit that provides an analytic standard error—and the per‐run damping ratios were fused by precision (inverse‐variance) weighting to obtain a single with 68% confidence intervals. Composition‐level results show a clear optimum at 0.3 wt% CB, where the fused damping ratio increased from 5.81 × 10 −3 (pure ABS) to 7.75 × 10 −3 (≈+33%), while the ultimate tensile strength rose from 9.83 to 18.12 MPa (≈+84%). At 1 wt%, the damping remained elevated but strength decreased; at 2 wt% both metrics declined, consistent with agglomeration observed in scanning electron microscope images. A strength–damping Pareto view highlights 0.3 wt% as a practical composition window for balanced performance in MEX ABS/CB parts. The workflow—multi‐estimator analysis with uncertainty‐aware fusion—provides reproducible damping estimates from short free‐decay records and can be applied to other printed polymers and fillers.

  • Research Article
  • 10.1126/sciadv.aea9701
Quantum interference of single photons without optical superposition: Toward high resolution imaging in spatial and spectral domains.
  • Apr 24, 2026
  • Science advances
  • Yunxiao Zhang + 9 more

Observation of the universe demands telescopes with high resolution. In the optical band, traditional interference requires bringing interfering fields together, which limits the resolution due to the restricted length of baseline. Here we demonstrate the very long-baseline interferometer (VLBI) in optical band, where two interfering fields never met each other. In particular, we report the first quantum interference observation when the input of VLBI is single-photon state. Interference is recovered after measuring the amplitudes of photon fields and digitally processing the signals of quantum receivers. Moreover, we analyze interference in time and spectral domains for broadband thermal light input and show that the ultrahigh spectral resolution can improve the precision of radial velocity to 0.08centimeters per second, which is 2 orders of magnitude better than that achievable at the current stage. Further, we apply the spectrally resolved interference in distinguishing two independent sources with angular resolutions beyond diffraction limit. Our investigations have a profound effect on the VLBI, quantum optics, and precision measurement.

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