Evolutionary spectral estimation based on adaptive use of weighted norms

摘要

In this paper, an evolutionary spectral estimator based on the application of Adaptive Weighted Norm Extrapolation (AWNE) is formulated and illustrated for analysis of nonstationary signals. The AWNE method produces a stationary extension of the data so that computing its Fourier transform yields a nonparametric, high-resolution spectrum estimate. The evolutionary formulation described here uses a time slice of the time-averaged Spectrogram to select the initial weight function (prior spectrum) used in AWNE for each block of data. This function strongly influences the final shape of the resulting spectrum. The resulting Short-Time AWNE (STAWNE) time-frequency representation yields improved frequency-domain resolution, preserves components which last longer than one time block, and is devoid of cross-terms. Comparison with short-time autoregressive spectral estimation yields improved consistency in the spectral energy levels as time varies. Finally, this sequential spectrum estimator is also illustrated for use in range-Doppler imaging of reflectivity surfaces having prominent scatterers by hybrid two-dimensional spectral estimation in-tandem with the discrete Fourier transform.