Sources of and remedies for spectral line splitting in autoregressive spectrum analysis

Abstract

Spectral line splitting in autoregressive spectral estimation changes what should be a single spectral line into two or more displaced spectral lines. Fougere was the first researcher to note the existence of certain conditions for sinusoidal data for which splitting occurred. He proposed a complicated gradient-descent algorithm which seems to fix the problem for at least one sinusoid. It is shown that spectral line splitting is a result of estimation errors and is not inherent in the autoregressive approach. In particular, the interaction between positive and negative sinusoidal frequency components in the Burg reflection coefficient and Yule-Walker auto-correlation estimates and the use of the biased autocorrelation estimator in the Yule-Walker approach is responsible for spectral line splitting. Spectral line splitting may be alleviated for one sinusoid by using complex data and also, the unbiased autocorrelation estimator in the Yule-Walker case. Spectral line splitting for multiple sinusoids is discussed.