Optimally averaging the interpolated fast fourier transform in both directions

The interpolated fast Fourier transform FFT (IpFFT) had been proposed to eliminate the picket fence effect of the fast Fourier transform. However, the modulus-based IpFFT (without windowing) is subjected to large bias in the condition of nearly coherent sampling condition. In addition, only the first and second highest spectral lines were used in most relevant references. The complex spectrum-based IpFFT is investigated. It is less sensitive to the interpolating direction error. Further, both directions of IpFFT can be averaged to decrease the estimation variance. The optimal weight required to minimise the estimation variance is established. The numerical simulation is carried out, and the results are compared with the Cramer-Rao bound.