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Determining light shift in Raman-Ramsey interference is important for the development of atomic frequency standards based on a vapor cell. We have accurately calculated light shift in Raman-Ramsey interference using the density-matrix…
A method for time-frequency analysis is given. The approach utilizes properties of Gaussian distribution, properties of Hermite polynomials and Fourier analysis. We begin by the definitions of a set of functions called harmonic Gaussian…
When using a finite difference method to solve an initial--boundary--value problem, the truncation error is often of lower order at a few grid points near boundaries than in the interior. Normal mode analysis is a powerful tool to analyze…
The non-equilibrium stationary coherences that form in donor-acceptor systems are investigated to determine their relationship to the efficiency of energy transfer to a neighboring reaction center. It is found that the effects of asymmetry…
Diverse synchronization dynamics within the grid-following (GFL)/grid-forming (GFM) converters-interlinked system are prone to induce oscillatory instabilities. To quantify their stability influences, frequency-domain modal analysis (FMA)…
A theory of transformation is presented for the diagonalization of a Hamiltonian that is quadratic in creation and annihilation operators or in coordinates and momenta. It is the systemization and theorization of Dirac and…
This work investigates the transient and dynamical behavior of hybrid AC/DC systems using dual-port grid-forming (GFM) control. A generalized modeling framework for hybrid AC/DC networks is first introduced that accounts for converter,…
The graph Hilbert transform (GHT) is a key tool in constructing analytic signals and extracting envelope and phase information in graph signal processing. However, its utility is limited by confinement to the graph Fourier domain, a fixed…
We consider the nonlinear Duffing oscillator in presence of fractional damping which is characteristic in different physical situations. The system is studied with a smaller and larger damping parameter value, that we call the underdamped…
In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…
In this paper, new insights in frequency-domain implementations of digital finite-length impulse response filtering (linear convolution) using overlap-add and overlap-save techniques are provided. It is shown that, in practical…
This study presents a physically informed hybrid time-frequency and machine learning (STFT-ML) framework for arc stability monitoring in electric arc welding systems. The primary current signal is modeled as a stochastic representation of…
This research work focuses on the design of a high-resolution fast Fourier transform (FFT) /inverse fast Fourier transform (IFFT) processors for constraints analysis purpose. Amongst the major setbacks associated with such high resolution,…
We study the localization properties of normal modes in harmonic chains with mass and spring weak disorder. Using a perturbative approach, an expression for the localization length is obtained, which is valid for arbitrary correlations of…
Time-frequency transforms represent a signal as a mixture of its time domain representation and its frequency domain representation. We present efficient algorithms for the quantum Zak transform and quantum Weyl-Heisenberg transform.
The modulation transfer function (MTF) is widely used to characterise the performance of optical systems. Measuring it is costly and it is thus rarely available for a given lens specimen. Instead, MTFs based on simulations or, at best, MTFs…
The increasing penetration of renewable energy leads to a continuous reduction in system inertia, for which conventional synchronization criteria based solely on frequency consistency can no longer accurately capture the coupled dynamics of…
If a disturbance rocks a low-inertia power system, the frequency decline may be too rapid to arrest before it triggers undesirable responses from generators and loads. In the worst case, this instability could lead to blackout and major…
A fast full-wave simulation technique is presented for the analysis of large irregular planar arrays of identical 3-D metallic antennas. The solution method relies on the Macro Basis Functions (MBF) approach and an interpolatory technique…
We provide an overview of high dimensional dynamical systems driven by random matrices, focusing on applications to simple models of learning and generalization in machine learning theory. Using both cavity method arguments and path…