Superresolution of Fourier transform spectra by autoregressive model fitting with singular value decomposition

Autoregressive model fitting with singular value decomposition is applied to the interferogram data measured by a Fourier transform spectrometer to estimate superresolving spectra. The interferogram data matrix is decomposed into singular values with eigenvectors and its generalized inverse matrix is used for estimating the coefficients of the autoregressive model. This method suppresses the noise component in the data and avoids the risk of producing spurious peaks, which were the problem inherent in our earlier work using the maximum entropy method [ Appl. Opt.22, 3593 ( 1983)]. The experimental results of superresolving spectral estimation are shown with the data of a visible emission spectrum and infrared absorption spectra.