Least squares phase estimation of mixed signals

Estimating the phase of sinusoids in noise in contrast to amplitude and frequency components has been less addressed in previous studies. In this paper, we derive the least squares phase estimator (LSPE) solution to recover the phase of an underlying signal observed in noise. Through Monte-Carlo simulations, we demonstrate the robustness of the proposed phase estimator against the modeling error. The proposed phase estimator is further evaluated in the speech enhancement setup to asses how much improvement is obtained by replacing the noisy phase with the LSPE when reconstructing the enhanced speech signal. Significant improvement in speech quality and speech intelligibility is obtained by replacing the noisy phase with the estimated phase provided by the proposed LSPE once the ambiguity in the phase candidates is removed.