Related papers: The spectrum decorrelation assumption for the cros…
We review the state space decomposition techniques for the assessment of the noise properties of autonomous oscillators, a topic of great practical and theoretical importance for many applications in many different fields, from electronics,…
In this paper, we describe a numerical continuation method that enables harmonic analysis of nonlinear periodic oscillators. This method is formulated as a boundary value problem that can be readily implemented by resorting to a standard…
The wave equation for vectors and symmetric tensors in spherical coordinates is studied under the divergence-free constraint. We describe a numerical method, based on the spectral decomposition of vector/tensor components onto spherical…
Based on the work done by an electromagnetic field on an atomic or molecular electronic system, a general gauge invariant formulation of transient absorption spectroscopy is presented within the semi-classical approximation. Avoiding…
The design and performance of a sensitive and reliable cross-correlation spectrum analyzer for studying low frequency transport noise is described in detail. The design makes use of common PC-based data acquisition hardware and…
Any frequency selective device with an ongoing drift will cause observed spectra to be variously and simultaneously scaled in proportion to their source distances. The reason is that detectors after the drifting selection will integrate…
We propose a decomposition method for the spectral peaks in an observed frequency spectrum, which is efficiently acquired by utilizing the Fast Fourier Transform. In contrast to the traditional methods of waveform fitting on the spectrum,…
A better understanding of the noise causing qubit decoherence is crucial for improving qubit performance. The noise spectrum affecting the qubit may be extracted by measuring dephasing under the application of pulse sequences but requires…
A practical constraint that comes in the way of spectrum estimation of a continuous time stationary stochastic process is the minimum separation between successively observed samples of the process. When the underlying process is not…
In this paper, we present an exact formalism for transient current-current correlations and transient noise spectra. The exact solution of transient current correlations in both the time domain and the frequency domain are obtained. Without…
We study a spectral initialization method that serves a key role in recent work on estimating signals in nonconvex settings. Previous analysis of this method focuses on the phase retrieval problem and provides only performance bounds. In…
We present a method, based on commutator methods, for the spectral analysis of uniquely ergodic dynamical systems. When applicable, it leads to the absolute continuity of the spectrum of the corresponding unitary operators. As an…
A definition of frequency (cycles per unit-time) based on an approximate reconstruction of the phase-space trajectory of an oscillator from a signal is introduced. It is shown to be invariant under linear filtering, and therefore…
We present a spectrogram separation method tailored for mixtures comprising two nonstationary components. By exploiting the unique characteristics of their time-frequency representations, we propose an inverse problem formulation to…
The measurements of very low level signals at low frequency is a very difficult problem, because environmental noise increases in this frequency domain and it is very difficult to filter it efficiently. In order to counteract these major…
Two iterative techniques are described for decomposing a long-slit spectrum into the individual spectra of the point sources along the slit and the spectrum of the underlying background. One technique imposes the strong constraint that the…
We discuss phase transitions in PT-symmetric optical systems. We show that due to frequency dispersion of the dielectric permittivity, an optical system can have PT-symmetry at isolated frequency points only. An assumption of the existence…
In the presence of interactions the frequency of a simple harmonic oscillator deviates from the noninteracting one. Various methods can be used to compute the changes to the frequency perturbatively. Some of them resemble the methods used…
Cross-spectral analysis is a mathematical tool for extracting the power spectral density of a correlated signal from two time series in the presence of uncorrelated interfering signals. We demonstrate and explain a set of conditions where…
Spectrum denoising is an important procedure for large-scale spectroscopical surveys. This work proposes a novel stellar spectrum denoising method based on deep Bayesian modeling. The construction of our model includes a prior distribution…