Sinusoid parameter estimation using the fast Fourier transform

The problem with using the FFT to do spectral estimation is that only a sampled version of the discrete Fourier transform of the input signal is provided. To do parameter estimation on a signal with frequency that does not appear at the output of the FFT, one has to perform spectral interpolation to approximate the original continuous spectrum. The author introduces a new interpolation scheme that allows the frequency and amplitude of a sinusoid to be estimated with high accuracy. The method is based on the fact that spectral convolution introduces spectral leakage that can be observed at the output of an FFT. With the minimum four-sample Blackman-Harris window, this method yields better results than the conventional parabola-fitting technique. The largest error occurs when the frequency is halfway between two frequency bins. Higher-order Taylor series could be used to improve the estimation in the range of 0.45<|ε|⩽0.5