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.

Technique for the evaluation of derivatives from noisy biomechanical displacement data using a model-based bandwidth-selection procedure.

Abstract: Smoothing and differentiation of noisy signals are common problems whenever it is difficult or impossible to obtain derivatives by direct measurement. In biomechanics body displacements are frequently assessed and these measurements are affected by noise. To avoid high-frequency noise magnification, data filtering before differentiation is needed. In the approach reported here an autoregressive model is fitted to the signal. This allows the evaluation of the filter bandwidth and the extrapolation of the data. The extrapolation also reduces edge effects. Low-pass filtering is performed in the frequency domain by a linear phase FIR filter and differentiation is performed in the frequency domain. The reported results illustrate the accuracy of the algorithm and its speed (mainly due to the use of the FFT algorithm). Automatic bandwidth selection also guarantees the homogeneity of the results.

The application of the discrete Fourier transform in the estimation of power spectra, coherence, and bispectra of geophysical data

Abstract: The computation of power spectra, cross spectra, coherence, and bispectra of various types of geophysical random processes is part of the established routine. Since it is routine, some of the standard procedures need to be examined rather carefully to be certain that the assumptions behind the procedures are applicable to the data on hand. The basic criteria for a particular method are its resolution bandwidth, its variance, and its bias. In this paper several basic power-spectrum estimation procedures are reviewed and their statistical and mathematical properties are discussed. The direct use of the discrete Fourier transform for various spectrum calculations is discussed in detail, and its properties are compared with the standard procedure that uses the cosine transform of the estimated correlation function.

Estimating Interharmonics by Using Sliding-Window ESPRIT

Abstract: A method is proposed for estimating inter-harmonic frequencies in power system voltage and current signals. The method is based on a spectrum-estimation method known as ldquoestimation of signal parameters via rotational invariance techniquesrdquo (ESPRIT). To allow for a more reliable spectral estimation and to cover nonstationarity in the signal, a sliding-window version of ESPRIT is introduced. This paper describes the basic ESPRIT method as well as sliding-window ESPRIT. The paper discusses the application of the method to one synthetic signal and three measurement signals. It is shown that the method allows for very accurate frequency estimation of interharmonic components. The limitations of the methods, such as line splitting and spurious components, can be overcome by using the coherent information obtained from the sliding-window method. A number of remaining issues are also discussed in this paper.

Bias‐corrected nonparametric spectral estimation

Abstract: . The theory of nonparametric spectral density estimation based on an observed stretch X1,…, XN from a stationary time series has been studied extensively in recent years. However, the most popular spectral estimators, such as the ones proposed by Bartlett, Daniell, Parzen, Priestley and Tukey, are plagued by the problem of bias, which effectively prohibits ✓N-convergence of the estimator. This is true even in the case where the data are known to be m-dependent, in which case ✓N-consistent estimation is possible by a simple plug-in method. In this report, an intuitive method for the reduction in the bias of a nonparametric spectral estimator is presented. In fact, applying the proposed methodology to Bartlett's estimator results in bias-corrected estimators that are related to kernel estimators with lag-windows of trapezoidal shape. The asymptotic performance (bias, variance, rate of convergence) of the proposed estimators is investigated; in particular, it is found that the trapezoidal lag-window spectral estimator is ✓N-consistent in the case of moving-average processes, and ✓(N/log/N)-consistent in the case of autoregressive moving-average processes. The finite-sample performance of the trapezoidal lag-window estimator is also assessed by means of a numerical simulation.