Sine wave fitting to short records initialized with the frequency retrieved from Hanning windowed FFT spectrum

The initial frequency is needed to execute an iterative approach to four-parameter sine wave fitting based on the least square error. An explicit formula to obtain the initial frequency is proposed to the case of short records, which makes use of three spectrum lines around the main lobe of the fast Fourier transform (FFT) weighted by the Hanning window (HW). This approach has been verified by simulation signals contaminated with different levels of noise. The noise free case shows the HW based approach is significantly more accurate than the approach based on the rectangular window (RW). However, the noise contaminated case shows the HW based approach is inferior to the RW based approach. In the same level of signal-to-noise ratio, the single-round-iteration variance with the HW based approach deviates off the Cramér–Rao bound at more cycles in record than that with the HW based.