An Advanced Optimal Spectral Estimation Algorithm in Fourier Spectroscopy with Application to Remote Sensing of the Atmosphere

Abstract

Remote sensing of the atmosphere from satellite to improve numerical weather prediction demands objective data handling methods, as the effectiveness of satellite data ultimately rests on our ability to process the data in real time. In this paper a procedure to recover high-resolution spectra from infrared Fourier spectrometer data is presented. The technique relies on the generalized cross-validation criterion and retains all the computational characteristics that are proper to the fast Fourier transform. The procedure yields adaptive apodizing functions that improve the convergence of the Fourier transform. Numerical examples are carried out using synthetic spectra computed by a high-resolution radiative transfer code. The effect of additive noise is also analyzed. The application of the technique to remote sensing of the atmosphere is discussed. Although our applications of the method emphasize the problem of recovering radiance spectra from interferogram signals, the procedure also applies in a general context, for example, to the estimation of variance spectra of stochastic processes from their autocovariance functions.