Against the long-range spectral leakage of the cosine window family

Suppressing spectral leakage in the fast Fourier transform (FFT) has been investigated for over 30 years. Regarding the frequently used cosine window family, it is observed that the long-range leakage sampled by FFT spectral lines follow a flat trajectory. Consequently, the long-range leakage is approximated by polynomials in this paper. In light of this parametric model, the interpolating formula is presented with up to nine-point for a cosine window with maximum side lobe decaying. Its expression is general in the window order and number of interpolating points. Some well-known formulas of the modulus-based interpolated FFT are parallel to special cases of the new formula, but the former are susceptible to significant bias at coherent sampling conditions. The new formula was tested with real-valued signals containing a single tone and then duel tones. It is demonstrated the new formula is easy to implement and is free of the significant bias aforementioned.