Using DFT and interpolation to reconstruct narrowband signals buried in noise

The DFT can be used to reconstruct narrowband signals buried in noise, even if the SNR in dB is very small or even negative, if the data sequence is long enough. By applying a frequency-dependent threshold which follows the contour of the DFT spectrum of the broadband background noise, one can extract the peak values of the DFT spectrum which represent amplitudes, frequencies, and phases of the sinusoids. Quadratic interpolation is used next to estimate the frequencies more exactly, which is especially useful when the frequency is not a DFT frequency. The estimated DFT spectrum is obtained by generating a spectral window having its main lobe centered at the estimated frequency. For cases where the background noise is not white, the authors model it as an AR process