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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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Journal ArticleDOI
TL;DR: A new smoothness priors long AR model method approach is taken to the short data span spectral estimation problem and the critical computation of the likelihood of the hyperparameters of the Bayesian model is realized by a constrained least squares computation.
Abstract: A new smoothness priors long AR model method approach is taken to the short data span spectral estimation problem. An autoregressive (AR) model that is relatively long compared to the data length is considered. The smoothness priors are in the form of the integrated squared derivatives of the AR model whitening filter. A smoothness tradeoff parameter or Bayesian hyperparameter balances the tradeoff between the infidelity of the AR model to the data and the infidelity of the model to the smoothness constraint. The critical computation of the likelihood of the hyperparameters of the Bayesian model is realized by a constrained least squares computation. Numerical examples are shown. The results of simulation studies using entropy comparison evaluations of the Bayesian and minimum AIC-AR methods of spectral estimation are also shown.

86 citations

Journal ArticleDOI
TL;DR: In this paper, an empirical study of the application of Akaike's final predictor error (FPE) criterion to the estimation of the order of finite autoregressive models to infinite auto-gressive model scheme data and the subsequent application of those models to spectral estimation are given.
Abstract: Results of an empirical study of the application of Akaike's final predictor error (FPE) criterion to the estimation of the order of finite autoregressive models to infinite autoregressive model scheme data and the subsequent application of those models to spectral estimation are given.

86 citations

Journal ArticleDOI
TL;DR: The discrete Fourier transform is applied as a coarse estimator of the frequency of a sine wave in Gaussian noise to estimate signal energy-to-noise density ratio E/N_0.
Abstract: The discrete Fourier transform (DFT) is applied as a coarse estimator of the frequency of a sine wave in Gaussian noise. Probability of anomaly and the variance of the estimation error are determined by computer simulation for several DFT block sizes as a function of signal energy-to-noise density ratio \mathcal{E}/N_0 . Several data windows are considered, but uniform weighting gives the best performance.

86 citations

Journal ArticleDOI
TL;DR: Simulation results show that accounting for the uncertainty of frequency estimates, rather than computing just point estimates, significantly improves the performance of VALSE, which is superior to that of state-of-the-art methods and closely approaches the Cramér-Rao bound computed for the true model order.
Abstract: We address the fundamental problem of line spectral estimation in a Bayesian framework. We target model order and parameter estimation via variational inference in a probabilistic model in which the frequencies are continuous-valued, i.e., not restricted to a grid; and the coefficients are governed by a Bernoulli-Gaussian prior model turning model order selection into binary sequence detection. Unlike earlier works which retain only point estimates of the frequencies, we undertake a complete Bayesian treatment by estimating the posterior probability density functions (pdfs) of the frequencies and computing expectations over them. Thus, we additionally capture and operate with the uncertainty of the frequency estimates. Aiming to maximize the model evidence, variational optimization provides analytic approximations of the posterior pdfs and also gives estimates of the additional parameters. We propose an accurate representation of the frequency pdfs by mixtures of von Mises pdfs, which yields closed-form expectations. We define the algorithm VALSE in which the estimates of the pdfs and parameters are iteratively updated. VALSE is a gridless, convergent method, does not require parameter tuning, can easily include prior knowledge about the frequencies and provides approximate posterior pdfs based on which the uncertainty in line spectral estimation can be quantified. Simulation results show that accounting for the uncertainty of frequency estimates, rather than computing just point estimates, significantly improves the performance. The performance of VALSE is superior to that of state-of-the-art methods and closely approaches the Cramer-Rao bound computed for the true model order.

86 citations

Journal ArticleDOI
TL;DR: The ability of the optimal kernel to suppress interference is quite remarkable, thus making the proposed framework potentially useful for interference suppression via time-frequency filtering.
Abstract: Current theories of a time-varying spectrum of a nonstationary process all involve, either by definition or by difficulties in estimation, an assumption that the signal statistics vary slowly over time. This restrictive quasistationarity assumption limits the use of existing estimation techniques to a small class of nonstationary processes. We overcome this limitation by deriving a statistically optimal kernel, within Cohen's (1989) class of time-frequency representations (TFR's), for estimating the Wigner-Ville spectrum of a nonstationary process. We also solve the related problem of minimum mean-squared error estimation of an arbitrary bilinear TFR of a realization of a process from a correlated observation. Both optimal time-frequency invariant and time-frequency varying kernels are derived. It is shown that in the presence of any additive independent noise, optimal performance requires a nontrivial kernel and that optimal estimation may require smoothing filters that are very different from those based on a quasistationarity assumption. Examples confirm that the optimal estimators often yield tremendous improvements in performance over existing methods. In particular, the ability of the optimal kernel to suppress interference is quite remarkable, thus making the proposed framework potentially useful for interference suppression via time-frequency filtering. >

86 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202316
202248
202159
2020101
201994
201895