AN ADAPTIVE DESIGN OF AN ALL - ZERO SPECTRAL ESTIMATOR Miguel

  • Jorge Girona Salgado
  • Published 2016

Abstract

An adaptive method to design a spectral estimator for signals showing an effectively lag-limited autocorrelation function is introduced. This procedure constitutes a parametric alternative to classical windowing and overlapping (WOSA) non-parametric methods of spectral estimation. The algorithm provides high quality results and it implies a low computational load; these facts justify an important position for the proposed method among both classical methods based on the periodogram and modern all-pole methods in cases in which the signal under analysis verifies the mentioned conditionofhaving an effectively finite duration autocorrelation function. · 19 81 V1NSPA Proce.edings A1/1/2 INTRODUCTION Given a finite set of samples of a zeromean, stationary stochastic process realization, {x(k)} , k = 0, ... , N1, an estimator of the power spectral density ·of the process is the FoUi~ier transform A 00 A Sxx (w) = L: r (1) exp( -jlw) 1=-oo XX (1) "' of the sequence {r (1)} , an estimator of the process autocorrelation function XX {rxx(l)} . The main problem in this estimation consist on processing {x(k)} , k = o, ... , N1, to obtain {r (1)}. A XX Sxx(w) must be a non-negative function for allw, since it estimates a power spectral density. To satisfy thi_s, it is necessary a form ()() r (1) = L: b(m + 1) b(m) XX m=-oo for the autocorrelation estimator. (2) Different methods of spectral estimation start from (2). The most widely originally used, based on the periodogram, is called Weighted Overlapped-Segment Averaging (WOSA) method {1} {2};itintroduces b(m) = w(m) x(m) (3) where {w(m)} , m= O, ... ,M, is a data window. This window can be applied with lengths less than N, forming {r (1)} by averaging the different functions XX obtained through (2). The methods that basically follow the above steps are considered nonparametric methods: they do not assume any previous knowledge about the class of process being analyzed. Nevertheless, we must remark that they force a finite duration {rxx(l)} . Other procedures, generally known as parametric methods, assume that {b(m)} is the impulse response of a linear system driven by a zero mean, unit variance white noise sequence {n(k)} . This point of view allows to relate directly the spectral estimation problem with the linear systems theory. In these cases, (2) can be interpreted as the autocorrelation of the output from the linear system

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Cite this paper

@inproceedings{Salgado2016ANAD, title={AN ADAPTIVE DESIGN OF AN ALL - ZERO SPECTRAL ESTIMATOR Miguel}, author={Jorge Girona Salgado}, year={2016} }