Interpolation Algorithms for Discrete Fourier Transforms of Weighted Signals

A new scheme is presented for the determination of the parameters that characterize a multifrequency signal. The essential innovation is that the signal is weighted before the discrete Fourier transform (DFT) is calculated from which the frequencies and complex amplitudes of the various components of the signal are obtained by interpolation. It is shown that by using the Hanning window for tapering substantial improvements are achieved in the following respects: i) more accurate results are obtained for interpolated frequencies, etc., ii) harmonic interference is much less troublesome even if many tones with comparable strengths are present in the spectrum, iii) nonperiodic signals can be handled without an a priori knowledge of the tone frequencies. The stability of the new method with respect to noise and arithmetic roundoff errors is carefully examined.