The relationship between AR-modelling bispectral estimation and the theory of linear prediction

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

1999

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In this paper we present a new autoregressive (AR) method for bispectrum estimation defined in terms of its third-moment sequence. The method is based on the segmentation of data into coupled records, and can be considered to be a modification of the``third order recursion method''(TOR). Its foundation resides in considering the data of the process at the left and the right of each record (needed for the calculation of third moment sequence) as not null and taking them as the data corresponding to the preceding and succeeding record respectively. Several simulated examples show that this method allows model parameters to be obtained with greater precision, most of all when only few data are available per record. The influence of factors such as number of data and records, model order, and added white and coloured Gaussian noise on the parameters' estimation is also considered.

Section: Bispectrum Estimation Using Ar-modelling 49 4 Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bispectrum estimation using AR‐modelling

Ruíz

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

1999

Self Cite

“…By minimizing this error with respect to the prediction coefficients, i.e. by imposing that dQ t f d a k 0 for k P 1Y p, and using the third-moments definition and the fact that x n is stationary, it can easily be obtained that (Gallego et al, 1994) gÀkY…”

Section: A Tor Equations Obtained By Fixed-order Minimizationmentioning

confidence: 99%

“…Thus, minimizing equation ( 10) with respect to b i , maintaining the fixed order p, and using only third moments over the m n plane we can similarly obtain the following matricial equation (Gallego et al, 1994):…”

Section: A Tor Equations Obtained By Fixed-order Minimizationmentioning

confidence: 99%

AR‐modelling bispectrum estimation – A comparison of existing methods and new contributions

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

Ruíz

2000

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This paper deals with bispectrum estimation via autoregressive (AR) modelling of a process contaminated by additive Gaussian noise (white and coloured). Two main contributions are provided in this work. First, a comparison between the existing third order recursion (TOR) and the constrained third order mean (CTOM) methods is presented. Basically, the second method is shown to be a smoothing windowed version (i.e. a covariance-type estimator) of the first one, achieved at the expense of the loss of the recursivity in the AR-model order. This prior analysis has induced us to develop an alternative scheme to tackle this type of problem, which, while maintaining the main feature of the CTOM method as a covariance type estimator, is a recursive-in-order algorithm. This recursivity is obtained carrying out an appropriate minimization procedure of some prediction squared errors also defined here. The paper also compares, by means of simulations, this proposed method and the two existing ones.

“…In (Gallego et al, 2005;Piotrkowski et al, 2005) we successfully evaluated the coating adherence by applying the WT to AE signals from scratch test (ST), specially in galvanized steel on as-cast hot-dip galvanized samples. High Order Spectral (HOS) analysis is applied in AE an in many areas because of its important advantages: it suppresses additive Gaussian noise (both white and colored), it renders information about the signal phase, it helps detecting and characterizing non-linearities and gaussianity deviations (Gallego et al, 1994;Gonzalez de la Rosa et al, 2005).…”

Section: Introductionmentioning

confidence: 99%

Wavelet Transform and Bispectrum Applied to Acoustic Emission Signals from Adherence Scratch-Tests on Corroded Galvanized Coatings

Gil

Vico

et al. 2006

AMR

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Wavelet analysis and bispectrum was applied to Acoustic Emission (AE) signals from scratch tests on corroded hot-dip galvanized samples in order to achieve the detection of corrosion products in pieces non reachable by visual inspection. AE signals were correlated with the fracture mechanisms occurring during scratch tests, while the contact force increased. Results were corroborated by Scanning Electron Microscopy (SEM), Energy Dispersive X-ray spectroscopy (EDX) and X-Ray Diffraction (XRD).