Strong consistency of recursive least square estimates on amplified harmonics for line spectrum

For a sampled signal with length n, it is shown that the method of maximum least-squares regressions on amplified harmonics yields estimates for discrete frequencies with the variance of order n ^-3 and with the bias of an order almost surely smaller than n ^-3/2 (log n)^1/2+δ. Hence, these estimates are strongly consistent and very accurate. It is shown that these estimates can also be obtained in an iterative way based on recursive least-squares estimates on amplified harmonics