DFT Interpolation for estimation of tone amplitudes and phases

An interpolation method is described for estimation of the frequency, amplitude and phase of a sinusoidal signal from the DFT of its discrete samples. It is shown that the scalloping loss, typically 1 db or more in tapered-window estimation, can be eliminated or substantially reduced. Also, robustness of this approach to noise is demonstrated by simulation examples and theoretical bounds. For multifrequency signals two different cases are treated. The first, where the frequencies of the sinusoids are known (such as in multifrequency radar detection), lends itself to closed form solution. In the second case, the constituent tone frequencies are estimated through interpolation, and then the amplitudes and phases are calculated as in the first case.