Phase noise mitigation in the autocorrelation estimates with data windowing: The case of two close sinusoids

Abstract

We address the phase noise and the superresolution problem in Toeplitz matrix-based spectral estimates. The Toeplitz autocorrelation (AC) matrix approach in spectral estimation brings in an order of magnitude computational advantage while the price paid is the phase noise that becomes effective at high signal-to-noise ratios (SNR). This noise can be mitigated with windowing the data though some concomitant loss in resolution occurs. The trade-offs between additive noise SNR, resolvability of sinusoids closer than the resolution limit, and behavior of the estimated AC lags and tone frequencies are investigated.