Related papers: Random Pulse Train Spectrum Calculation Unleashed
Here, we present a new method to evaluate the expectation value of the power spectrum of a time series. A statistical approach is adopted to define the method. After its demonstration, it is validated showing that it leads to the known…
The power density spectrum of a light curve is often calculated as the average of a number of spectra derived on individual time intervals the light curve is divided into. This procedure implicitly assumes that each time interval is a…
The detection of irregularly spaced pulses of non-negligible width is a fascinating yet under-explored topic in signal processing. It sits adjacent to other core topics such as radar and symbol detection yet has its own distinctive…
The temporal dynamics of ultrashort pulses are a fundamental feature in ultrafast optics. These dynamics can often be extracted from a two-dimensional trace consisting of a set of nonlinear spectra, using an iterative algorithm. Typically,…
We derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary length. The implications of our results to the structural and dynamical properties of networks…
Emission spectrum is calculated for a weak axisymmetric pulsar. Also calculated are the observed spectrum, efficiency, and the observed efficiency. The underlying flow of electrons and positrons turns out to be curiously intricate.
We present a new method for generating a regular train of ultrashort optical pulses in a prepared two-level medium. The train develops from incident monochromatic probe radiation travelling in a medium of atoms, which are in a quantum…
I study how pulse to pulse phase coherence in a pulse train can survive super-broadening by extreme self phase modulation (SPM). Such pulse trains have been used in phase self-stabilizing schemes as an alternative to using a feedback…
We analyze the power spectral density of a signal composed of nonoverlapping rectangular pulses. First, we derive a general formula for the power spectral density of a signal constructed from the sequence of nonoverlapping pulses. Then we…
The relationship between the spectral density and free energy of a spin system is considered. The analytical expressions allowing for the calculation of the spectral density for solvable models are determined. A linear Ising model is taken…
Spectral estimation (SE) aims to identify how the energy of a signal (e.g., a time series) is distributed across different frequencies. This can become particularly challenging when only partial and noisy observations of the signal are…
.Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments…
This paper investigates the problem of estimating the spectral power parameters of random analog sources using numerical measurements acquired with minimum digitization complexity. Therefore, spectral analysis has to be performed with…
A statistical model of discrete finite length random processes with negative power law spectral densities is presented. The definition of terms is followed by a description of the spectral density trend. An algorithmic construction of…
Intense, well-controlled regular light pulse trains start to play a crucial role in many fields of physics. We theoretically demonstrate a very simple and robust technique for generating such periodic ultrashort pulses from a continuous…
The measurement of electron cloud densities in particle accelerators using microwaves has proven to be an effective, non-invasive and inexpensive method. So far the experimental schemes have used continuous waves. This has either been in…
This article contains two main theoretical results on neural spike train models. The first assumes that the spike train is modeled as a counting or point process on the real line where the conditional intensity function is a product of a…
The power spectrum analysis of spectral fluctuations in complex wave and quantum systems has emerged as a useful tool for studying their internal dynamics. In this paper, we formulate a nonperturbative theory of the power spectrum for…
We consider reversible random walks in random environment obtained from symmetric long--range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and…
We present a general procedure for obtaining the present density fluctuation probability distribution given the statistics of the initial conditions. The main difficulties faced with regard to this problem are those related to the…