Topic
Spectral density estimation
About: Spectral density estimation is a research topic. Over the lifetime, 5391 publications have been published within this topic receiving 123105 citations.
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TL;DR: This work proves that the clarity and precision by which the CTF can be detected using periodogram averaging and autoregressive modelling is far better than by any conventional method based on the Fourier transform amplitude alone.
61 citations
TL;DR: A double image encryption method is proposed by utilizing discrete multiple-parameter fractional Fourier transform and chaotic maps to encrypt two original images scrambled by one chaotic map with one original image as its phase.
61 citations
TL;DR: In this article, two methods for estimating a whitening filter for ground-based gravitational wave detectors with the goal of performing parameter estimation studies were compared and compared with the statistics of the data used for gravitational wave parameter estimation.
Abstract: Estimating the parameters of gravitational wave signals detected by ground-based detectors requires an understanding of the properties of the detectors' noise. In particular, the most commonly used likelihood function for gravitational wave data analysis assumes that the noise is Gaussian, stationary, and of known frequency-dependent variance. The variance of the colored Gaussian noise is used as a whitening filter on the data before computation of the likelihood function. In practice the noise variance is not known and it evolves over timescales of dozens of seconds to minutes. We study two methods for estimating this whitening filter for ground-based gravitational wave detectors with the goal of performing parameter estimation studies. The first method uses large amounts of data separated from the specific segment we wish to analyze and computes the power spectral density of the noise through the mean-median Welch method. The second method uses the same data segment as the parameter estimation analysis, which potentially includes a gravitational wave signal, and obtains the whitening filter through a fit of the power spectrum of the data in terms of a sum of splines and Lorentzians. We compare these two methods and conclude that the latter is a more effective spectral estimation method as it is quantitatively consistent with the statistics of the data used for gravitational wave parameter estimation while the former is not. We demonstrate the effect of the two methods by finding quantitative differences in the inferences made about the physical properties of simulated gravitational wave sources added to LIGO-Virgo data.
60 citations
01 Jan 1979
TL;DR: In this paper, the authors proposed prediction error filtering and maximum-entropy spectral estimation for ARMA spectral estimation, and applied the maximum likelihood method and the maximum entropy method to array processing.
Abstract: Prediction-error filtering and maximum-entropy spectral estimation.- Autoregressive and mixed autoregressive-moving average models and spectra.- Iterative least-squares procedure for ARMA spectral estimation.- Maximum-likelihood spectral estimation.- Application of the maximum-likelihood method and the maximum-entropy method to array processing.- Recent advances in spectral estimation.
60 citations
TL;DR: A D-fold Hankel matrix is constructed from the measurements and exploited to exploit its Vandermonde decomposition in the noiseless case, and numerical experiments show that the noise tolerance of MUSIC obeys a power law with the minimum separation of frequencies.
Abstract: This paper presents a performance analysis of the MUltiple SIgnal Classification (MUSIC) algorithm applied on $D$ dimensional single-snapshot spectral estimation while $s$ true frequencies are located on the continuum of a bounded domain. Inspired by the matrix pencil form, we construct a D-fold Hankel matrix from the measurements and exploit its Vandermonde decomposition in the noiseless case. MUSIC amounts to identifying a noise subspace, evaluating a noise-space correlation function, and localizing frequencies by searching the $s$ smallest local minima of the noise-space correlation function. In the noiseless case, $(2s)^{D}$ measurements guarantee an exact reconstruction by MUSIC as the noise-space correlation function vanishes exactly at true frequencies. When noise exists, we provide an explicit estimate on the perturbation of the noise-space correlation function in terms of noise level, dimension $D$ , the minimum separation among frequencies, the maximum and minimum amplitudes while frequencies are separated by 2 Rayleigh Length (RL) at each direction. As a by-product the maximum and minimum non-zero singular values of the multidimensional Vandermonde matrix whose nodes are on the unit sphere are estimated under a gap condition of the nodes. Under the 2-RL separation condition, if noise is i.i.d. Gaussian, we show that perturbation of the noise-space correlation function decays like $\sqrt{\log(\#({\bf N}))/\#({\bf N})}$ as the sample size $\#({\bf N})$ increases. When the separation among frequencies drops below 2 RL, our numerical experiments show that the noise tolerance of MUSIC obeys a power law with the minimum separation of frequencies.
60 citations