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: In this paper, it is shown that the problem of choosing the variance of the planewave complex amplitude and the noise covariance matrix jointly, to maximize the likelihood function for the observations, has no unique solution.
Abstract: The maximum likelihood method of frequency-wavenumber spectral estimation (MLM) is a high-resolution alternative to conventional Fourier analysis. This paper provides a new interpretation for MLM. The point of view taken is that at each wavenumber we attempt to estimate the power of a discrete planewave at that wavenumber, a problem complicated by the presence of interfering energy at other wavenumbers (noise), with an unknown spectral density matrix. It is shown that, subject to some assumptions, the problem of choosing the variance of the planewave complex amplitude (that is, the plane-wave power) and the noise covariance matrix jointly, to maximize the likelihood function for the observations, has no unique solution. There is a continuous range of values for the estimates all of which have the same (maximum) likelihood, the lower bound on the planewave power estimate being zero, and the upper bound being the MLM power estimate. Some important differences between the problem of estimating the planewave complex amplitude for each independent data segment and the problem of estimating the variance of the planewave complex amplitude are indicated.
81 citations
TL;DR: In this paper, a new time series bootstrap scheme, the Time Frequency Toggle (TFT)-Bootstrap, is proposed, which is based on bootstrapping the Fourier coecients of the observed time series, and then back-transforming them to obtain a bootstrap sample in the time domain.
Abstract: A new time series bootstrap scheme, the Time Frequency Toggle (TFT)-Bootstrap, is proposed. Its basic idea is to bootstrap the Fourier coecients of the observed time series, and then back-transforming them to obtain a bootstrap sample in the time domain. Related previous proposals, such as the ‘surrogate data’ approach, resampled only the phase of the Fourier coecients, and thus had only limited validity. By contrast, we show that the appropriate resampling of phase and magnitude in addition to some smoothing of Fourier coecients yields a bootstrap scheme that mimics the correct second-order moment structure for a large class of time series processes. As a main result we obtain a functional limit theorem for the TFT-Bootstrap under a variety of popular ways of frequency domain bootstrapping. Possible applications of the TFT-Bootstrap naturally arise in change-point analysis and unit-root testing where statistics are frequently based on functionals of partial sums. Finally, a small simulation study explores the potential of the TFT-Bootstrap for small samples showing that for the discussed tests in change-point analysis as well as unit-root testing it yields better results than the corresponding asymptotic tests if measured by size and power.
80 citations
TL;DR: This work investigates the stochastic resonance phenomenon in a physical system based on a tunnel diode and observes both a regime described by the linear-response theory and the nonlinear deviation from it.
Abstract: We investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode. The experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an interval of values spanning several orders of magnitude. We observe both a regime described by the linear-response theory and the nonlinear deviation from it. In the nonlinear regime we detect saturation of the power spectral density of the output signal detected at the frequency of the modulating signal and a dip in the noise level of the same spectral density. When these effects are observed we detect a phase and frequency synchronization between the stochastic output and the deterministic input.
80 citations
TL;DR: This behavior is predicted by a model in which the threshold is governed, not by local contrast or any other feature in the stimulus domain, but rather by the component of maximum magnitude in the two-dimensional Fourier transforms of these stimulus patterns.
80 citations
TL;DR: In this article, the Capon and the APES spectral estimators are combined for estimation of both the amplitude and the frequency of spectral lines, which is computationally simpler than APES and has about the same complexity as Capon.
Abstract: We propose combining the Capon and the APES spectral estimators for estimation of both the amplitude and the frequency of spectral lines. The so-obtained estimator does not suffer from Capon's biased amplitude estimates nor from APES' biased frequency estimates or resolution problem. Furthermore, the combined estimator is computationally simpler than APES and has about the same complexity as Capon. Numerical simulations are presented illustrating the increased performance.
80 citations