Fourier transform spectroscopy is nowadays able to produce spectra with extremely high signal-to-noise ratios, and thus extremely high information content. Unfortunately, this information is partially lost because of a lack of sufficiently effective line-narrowing methods to resolve overlapping spectral lines. A novel, and very promising, approach to the problem is the LOMEP line-narrowing method, based on consecutive linear prediction; the line narrowing is carried out in the signal domain by extrapolating the Fourier transform of the spectrum. However, LOMEP is not yet optimal. For example, it does not make use of the information contained in the output line shapes to correct the errors made in linear prediction. In fact, that procedure would not even be possible by using the prediction strategy adopted by LOMEP. Therefore it is possible to considerably improve the method by including the information contained in the distortions of the output spectral lines. In this paper a new method of line narrowing is presented, based on progressive improvement of the prediction until the output is free from distortions. The method is very easy to use and does not require a profound understanding of the underlying mathematics.

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