Noise compensation for autoregressive spectral estimates

The autoregressive spectral estimator possesses excellent resolution properties for time series which satisfy the "all-pole" assumption. When noise is added to the time series under analysis, the resolution of the spectral estimator decreases rapidly as the signal-to-noise ratio decreases. The usual approach to this problem is to model the resulting time series by the more appropriate autoregressive-moving average process and to use standard time series analysis techniques to identify the autoregressive parameters. This standard technique, however, does not result in a positive-definite autocorrelation matrix. As a result, it is shown that the resulting spectral estimator may exhibit a large increase in variance. An alternative approach, termed the noise compensation technique, is proposed. It attempts to correct the estimated reflection coefficients for the effect of white noise, assuming the noise variance is known or can be estimated. Simulation results indicate that a significant decrease in the degrading effects of noise may be realized using the noise compensation technique.

[1]  A. Wald,et al.  On the Statistical Treatment of Linear Stochastic Difference Equations , 1943 .

[2]  F. Hohn,et al.  Elementary Matrix Algebra , 1959 .

[3]  F. Downton,et al.  Time-Series Analysis. , 1961 .

[4]  F. Downton,et al.  Time Series Analysis , 1961, Mathematical Gazette.

[5]  J. P. Burg,et al.  Maximum entropy spectral analysis. , 1967 .

[6]  D. G. Watts,et al.  Spectral analysis and its applications , 1968 .

[7]  Will Gersch,et al.  Estimation of the autoregressive parameters of a mixed autoregressive moving-average time series , 1970 .

[8]  R. Lacoss.  DATA ADAPTIVE SPECTRAL ANALYSIS METHODS , 1971 .

[9]  J. C. Chow.  On estimating the orders of an autoregressive moving-average process with uncertain observations , 1972 .

[10]  A. Gray,et al.  On autocorrelation equations as applied to speech analysis , 1973 .

[11]  V. Pisarenko.  The Retrieval of Harmonics from a Covariance Function , 1973 .

[12]  J. Makhoul,et al.  Linear prediction: A tutorial review , 1975, Proceedings of the IEEE.

[13]  T. Ulrich,et al.  Maximum entropy spectral analy-sis and autoregressive decomposition , 1975 .

[14]  Albert H Nuttall,et al.  Spectral Analysis of a Univariate Process with Bad Data Points, via Maximum Entropy and Linear Predictive Techniques , 1976 .

[15]  John E. Markel,et al.  Linear Prediction of Speech , 1976, Communication and Cybernetics.

[16]  Antonio Cantoni,et al.  Properties of the Eigenvectors of Persymmetric Matrices with Applications to Communication Theory , 1976, IEEE Trans. Commun..

[17]  L. Marple.  Resolution of conventional Fourier, autoregressive, and special ARMA methods of spectrum analysis , 1977 .

[18]  Steven Kay,et al.  The effects of noise on the autoregressive spectral estimator , 1979 .