Study on Hanning window employed in interpolated FFTalgorithm

When using FFT for harmonic analysis,spectrum leakage and picket-fence effect make the results almost meaningless during non-synchronous sampling.By employing windows with small side-lobes,the leakage can be largely reduced.With the precondition that the effect of leakage is negligible,picket-fence effect can be overcome by interpolating the discrete spectrum.Firstly,this paper derives the exact expression of the spectrum of Hanning window,which reveals that Hanning window has strict linear phase under the main-lobe.Secondly,an approximate expression is obtained,which is so precise even when N is small(e.g.,N = 16).In addition,within the frequency range concerned,via the Taylor series expansion,gets an approximate polynomial expression,which features much less calculation and no 0/0 condition.Finally,provides interpolation formulas for frequency,amplitude and phase.Simulation result shows that the algorithm essentially eliminates the method error caused by non-synchronous sampling.