Eliminating white noise in spectra: A generalized maximum-entropy approach

In linear filtering, high-frequency (white) noise is reduced by apodization, which is the attenuation or elimination of high-order Fourier coefficients followed by an inverse transformation. Unfortunately, apodization requires compromises to be made among noise leakage, information loss, and Gibbs oscillations. These shortcomings are avoided with the corrected maximum-entropy (CME) procedure, but this procedure applies only to Lorentzian or approximately Lorentzian features. We develop a generalized maximum-entropy method based on partial Hilbert transforms that allows CME to be applied to any spectrum, thereby eliminating white-noise completely with no deleterious side effects. As Hilbert transforms are exact Kramers–Kronig replicas of the original endpoint-discontinuity-corrected segment, new spectral processing opportunities are also realized.