Complementary Complex-Valued Spectrum for Real-Valued Data: Real Time Estimation of the Panorama Through Circularity-Preserving Dft

Abstract

This work sheds a new light on the spectral whitening effects of the sliding discrete Fourier transform (DFT) and uses it as a basis for a novel technique for circularity-preserving spectral estimation. This makes it possible to utilise full available spectral information, unlike the existing methods which ignore the phase spectrum. We then use the so introduced circularity-preserving DFT to show that the Wiener filter can be used to estimate the recently introduced second-order complementary spectral measure, termed the panorama, even in the critical cases of short data windows and incoherent sampling. Numerical examples demonstrate the ability of the proposed procedure to estimate the spectral circularity and the panorama, even in a streaming-data setting for which the current methods are inadequate.