On Linear Prediction Models Constrained to Have Unit-Modulus Poles and Their Use for Sinusoidal Frequency Estimation

Linear prediction models with their poles restricted to the unit circle can be efficiently determined by using the Levinson or the split Levinson algorithm. A simple proof of this property is presented. The prime application of linear prediction models constrained to have unit-modulus poles is the estimation of sinusoidal frequencies. The consistency properties of the corresponding frequency estimates are analyzed. It is shown that in the presence of noise, the estimates are inconsistent and an explicit expression for the asymptotic bias is provided.