Nonparametric Spectral Estimation Methods Research Articles

A comparative study of non-parametric spectral estimators for application in machine vibration analysis

The vibration of a machine carries important information about the health of its internal components; this information, if properly extracted, can be extremely useful in the detection of developing faults within the machine. One of the most effective methods to extract this information is the computation of the vibration power spectrum, but since the statistical properties of the vibration signal are generally unknown, the power spectrum has to be estimated from the available finite-length data. A number of methods have been proposed for vibration spectral estimation, each presenting advantages and disadvantages. In each specific application, it is often necessary to evaluate and choose the optimum spectral estimation method. This paper presents an analysis of four widely accepted non-parametric spectral estimation methods: Periodogram, Blackman-Tukey, Welch, and Nuttall-Carter. It compares them based on their mean, variance, resolution, and computational requirements. It is found that all methods, except the Periodogram, can achieve the same mean, variance, and resolution but differ in leakage suppression and computational complexity. The Welch method has the best leakage suppression and the Nuttall-Carter method has the lowest computational burden in most cases.

Directional Wave Spectra Estimation in a Marginal Ice Zone Using Linear Prediction

Abstract A synthetic aperature radar (SAR) image of a wave field penetrating a marginal ice zone off Newfoundland was analyzed in order to get insight into the physical processes responsible for the swell attenuation. The analysis was done using a parameteric spectral-density estimation technique based on linear prediction. This approach allows the estimation of the directional spectrum of the swell on small images with a better low-frequency definition than nonparametric spectral estimation methods like fast Fourier transforms, resulting in a greater number of estimations over the wave propagation length. This increase in spatial resolution allowed the detection of physical phenomena occurring inside the ice pack that affected wave propagation. Evidence of wave refraction was observed inside the marginal ice zone as the waves encountered an area of different ice compaction. Finally, results show that the parametric approach leads to an evaluation of the attenuation coefficient similar to FFT analysis.

Spectral estimation of irregularly sampled multidimensional processes by generalized prolate spheroidal sequences

A nonparametric spectral estimation method is presented for bandlimited random processes that have been sampled at arbitrary points in one or more dimensions. The method makes simultaneous use of several weight sequences that depend on the set of sampling point, the signal band, and the frequency band being analyzed. These sequences are solutions to a generalized matrix eigenvalue problem and are termed generalized prolate spheroidal sequences, being extensions of the familiar discrete prolate spheroidal sequences. Statistics of the estimator are derived, and the tradeoff among bias, variance, and resolution is quantified. The method avoids several problems typically associated with irregularly sampled data and multidimensional processes. A related method is suggested that has nearly as good performance while requiring significantly fewer computations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Computationally lag-invariant recursive spectrum estimators

This paper is concerned with Fourier-based nonparametric spectral estimation methods for time-varying environments. It presents a class of interactive spectrum estimators in which the number of computations required to update the estimate at every data sample is independent of the number of the autocorrelation lags employed to produce this estimate. These estimators are termed lag invariant and form an important class due to their computational simplicity. Because of the lag-invariant property, resolution enhancement is achieved without additional cost in computations per frequency sample. The proposed class of recursive spectral estimators is based on specific selection of the lagged product windows used in the autocorrelation function estimation. In this paper, the conditions necessary to produce the lag-invariance property are delineated.