The cause of line splitting in Burg maximum-entropy spectral analysis

Burg´s algorithm for maximum-entropy autoregressive spectral estimation is analyzed for the case of one and two complex sinusoidal signals in additive white noise. In the latter case, two biases are found which can account for the line splitting and line shifting that occur in simulation studies when the SNR is very high. These biases vanish completely if the two complex sinusoids are in phase quadrature at the middle of the data record. If the data record contains an integral number of half-cycles of the difference frequency, the magnitude of the power spectral estimate will be biased, although the effects believed to cause splitting and shifting will be eliminated. For infinite SNR, the effect of these biases is to prevent perfect cancellation of the coherent signal by the correct-order Burg prediction-error filter (PEF). Then higher order PEF´s can be based on the uncancelled signal. It is conjectured that the severity of splitting and shifting is closely related to the relative magnitude of the uncancelled signal. Results of simulation studies to verify this conjecture are presented. The analysis also shows that lengthening the observation interval by including more data recorded at the original sampling rate should reduce the magnitude of the biases, but that increasing the number of data by increasing the sampling rate, while maintaining the observation interval unchanged, is of little use.