Significance of group delay functions in spectrum estimation

Abstract

A method of spectrum estimation using group delay functions is proposed. 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 wrappings, but the group delay function can be processed to derive significant information such as peaks in the spectral envelope. In the resulting spectral estimates obtained 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. The method works even for high noise levels. The results of this procedure are demonstrated through two illustrative examples: estimation of sinusoids in noise and estimation of the narrowband autoregressive process in noise.