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The evaluation of the spectral components of a signal by means of a DFT or FFT algorithm is subject to leakage errors whenever the sampling frequency is not coherent with the signal frequency. Smoothing windows are used to mitigate these errors, and interpolation methods are applied, in the frequency domain, to reduce these errors further on. However, if cosine windows are employed, closed-form formulas for the evaluation of the harmonic frequencies can be used only with second-order windows, while approximated formulas have to be used in the other cases. In both cases, a high computation burden is required. This paper proposes a fast interpolation method, independent of the window type and order, based on suitable look-up tables. Experimental results are reported and the accuracy is discussed, proving that the method provides results as good as those obtained with other methods, without requiring the same high computation burden.