Adaptive Filter-bank Approach to Restoration and Spectral Analysis of Gapped Data*

The main topic of this paper is the nonparametric estimation of complex (both amplitude and phase) spectra from gapped data, as well as the restoration of such data. The focus is on the extension of the APES (amplitude and phase estimation) approach to data sequences with gaps. APES, which is one of the most successful existing nonparametric approaches to the spectral analysis of full data sequences, uses a bank of narrowband adaptive (both frequency and data dependent) filters to estimate the spectrum. A recent interpretation of this approach showed that the filterbank used by APES and the resulting spectrum minimize a least-squares (LS) fitting criterion between the filtered sequence and its spectral decomposition. The extended approach, which is called GAPES for somewhat obvious reasons, capitalizes on the aforementioned interpretation: it minimizes the APES-LS fitting criterion with respect to the missing data as well. This should be a sensible thing to do whenever the full data sequence is stationary, and hence the missing data have the same spectral content as the available data. We use both simulated and real data examples to show that GAPES estimated spectra and interpolated data sequences have excellent accuracy. We also show the performance gain achieved by GAPES over two of the most commonly used approaches for gapped-data spectral analysis, viz., the periodogram and the parametric CLEAN method.