Related papers: The spectrum decorrelation assumption for the cros…
The average spectrum method is a promising approach for the analytic continuation of imaginary time or frequency data to the real axis. It determines the analytic continuation of noisy data from a functional average over all admissible…
We focus on an alignment-free method to estimate the underlying signal from a large number of noisy randomly shifted observations. Specifically, we estimate the mean, power spectrum, and bispectrum of the signal from the observations. Since…
The useful dynamic range of an image in the diffraction limited regime is usually limited by speckles caused by residual phase errors in the optical system forming the image. The technique of speckle decorrelation involves introducing many…
A method is proposed for obtaining the spectrum for noise that causes the phase decoherence of a qubit directly from experimentally available data. The method is based on a simple relationship between the spectrum and the coherence time of…
This paper presents a general framework for modeling dependence in multivariate time series. Its fundamental approach relies on decomposing each signal in a system into various frequency components and then studying the dependence…
The output of oscillators is usually not stable over time. In particular, phase variations---or \emph{phase noise}---corrupts the oscillations. In this letter, we describe a circuit that designed to average the phase noise processes and…
The noise of a device under test (DUT) is measured simultaneously with two instruments, each of which contributes its own background. The average cross power spectral density converges to the DUT power spectral density. This method enables…
A new method to calculate the spectrum using cascaded open systems and master equations is presented. The method uses two state analyzer atoms which are coupled to the system of interest, whose spectrum of radiation is read from the…
Phase response curves are important for analysis and modeling of oscillatory dynamics in various applications, particularly in neuroscience. Standard experimental technique for determining them requires isolation of the system and…
We study an underdamped oscillator with shot-noise frequency fluctuations. The oscillator spectrum is determined by the interference of the susceptibilities for different eigenfrequencies. Depending on the parameters, it has a fine…
This article deals with the erratic and inconsistent phase-noise spectra often seen in low-noise oscillators, whose floor is of the order of $-180$ dBc/Hz or less. Such oscillators are generally measured with two-channel instruments based…
This article addresses the measurement of the power spectrum of red noise processes at the lowest frequencies, where the minimum acquisition time is so long that it is impossible to average on a sequence of data record. Therefore, averaging…
Precise spectroscopy of oscillating fields plays significant roles in many fields. Here, we propose an experimentally feasible scheme to measure the frequency of a fast-oscillating field using a single-qubit sensor. By invoking a stable…
Both sampling a time-varying signal, and its spectral analysis are activities subjected to theoretically compelling, such as Shannon's theorem and the objectively limiting of the frequency's resolution. Usually, the signals' spectra are…
The cross-spectrum method consists in measuring a signal $c(t)$ simultaneously with two independent instruments. Each of these instruments contributes to the global noise by its intrinsec (white) noise, whereas the signal $c(t)$ that we…
We propose a cross-correlation method for the searches of ultra-light fields, in particular, with a space network of atomic sensors. The main motivation of the approach is cancellation of uncorrelated noises in the observation data and…
An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicate the intrinsic limitations of spectral methods when it comes…
The main purpose of this article is to alert spectroscopists, particularly those involved in surveys, to the fact that rapidly pulsating sources induce periodic structures in spectra. This would allow the detection of new classes of objects…
The Fourier series method is used to solve the homogeneous equation governing the motion of the harmonic oscillator. It is shown that the general solution to the problem can be found in a surprisingly simple way for the case of the simple…
We have developed a new methodology and a time-domain software package for the estimation of the oscillation frequency and the phase noise spectrum of non-linear noisy microwave circuits based on the direct integration of the system of…