Significance of group delay functions in spectrum estimation

In this paper we propose a method of snectrum estimation using group delay functions. This method exploits the additive property of the Fourier transform (FT) phase to extract spectral information of the signal in the presence of noise. The phase is generally featureless due to random polarity and wrapping; but the group delay function can be processed to derive significant information such as peaks in the spectral envelope. In the spectral estimates obtained using this method, the resolution properties of the periodogram estimate are preserved while the variance is reduced. Variance caused by the sidelobe leakage due to windows and additive noise are significantly reduced even in the spectral estimate obtained using a single realization of the observation peak. Resolution is primarily dictated by the size of the data window according to the standard time bandwidth product relation. The method works even for high noise levels (SNR = 0 dB or less). The results of this spectrum estimation procedure are demonstrated through several illustrative examples. In particular, two cases are considered namely, 1) estimation of sinusoids in noise and 2) estimation of the narrow-band autoregressive process in noise. ? 1992 IEEE