Combining the Hanning windowed interpolated FFT in both directions

The interpolated fast Fourier transform (IFFT) has been proposed as a way to eliminate the picket fence effect (PFE) of the fast Fourier transform. The modulus based IFFT, cited in most relevant references, makes use of only the 1st and 2nd highest spectral lines. An approach using three principal spectral lines is proposed. This new approach combines both directions of the complex spectrum based IFFT with the Hanning window. The optimal weight to minimize the estimation variance is established on the first order Taylor series expansion of noise interference. A numerical simulation is carried out, and the results are compared with the Cramer-Rao bound. It is demonstrated that the proposed approach has a lower estimation variance than the two-spectral-line approach. The improvement depends on the extent of sampling deviating from the coherent condition, and the best is decreasing variance by 2/7. However, it is also shown that the estimation variance of the windowed IFFT with the Hanning is significantly higher than that of without windowing.