Fast procedures for accurate parameter estimation of sine-waves affected by noise and harmonic distortion

In this paper two procedures are proposed for the estimation of the frequency, amplitude, and phase of sine-waves affected by either wideband noise or by both noise and harmonic distortion, respectively. The procedures are very simple and suitable for real-time applications. According to them, firstly the signal parameters are estimated by means of the new Corrected Interpolated Discrete Fourier transform (IpDFTc) algorithm, which compensates the contribution of the spectral interference from the fundamental image component and harmonics on the parameter estimates returned by the classical IpDFT algorithm. Then, a linear sine-fit algorithm is applied to optimize the noise robustness of the estimators, which is worsened by signal windowing employed to reduce the effect of spectral leakage on the IpDFTc estimates. In the paper, the Hann window is applied since it exhibit both the highest noise robustness among the Maximum Sidelobe Decay (MSD) windows and a good reduction of long-range spectral leakage. It has been shown that both proposed procedures almost attain the Cramér-Rao Lower Bounds (CRLBs) for unbiased estimators when at least about 1.5 sine-wave cycles are observed so that the effect of interfering tones on the IpDFTc estimates can be effectively compensated by windowing. The performances of both procedures are analysed through computer simulations and experimental results.