Elimination of endpoint-discontinuity artifacts in the analysis of spectrain reciprocal space

Reciprocal-space analysis offers several advantages for determining critica l point parameters in optical and other spectra, for example the separation of baseline effects, information, and noise in low-, medium-, and high-ind ex Fourier coefficients, respectively. However, endpoint-discontinuity arti facts can obscure much of the information when segments are isolated for an alysis. We developed a procedure for eliminating these artifacts and recove ring buried information by minimizing in the white-noise region the mean-sq uare deviation between the Fourier coefficients of the data and those of lo w-order polynomials, then subtracting the resulting coefficients from the d ata over the entire range. We find that spectral analysis is optimized if n o false data are used, i.e., when the number of points transformed equals t he number of actual data points in the segment. Using fractional differenti ation we develop a simple derivation of the variation of the reciprocal-spa ce coefficients with index n for Lorentzian and Gaussian line shapes in dir ect space. More generally, we show that the definition of critical point en ergies in terms of phase coherence of the Fourier coefficients allows these energies to be determined for a broad class of line shapes even if the dir ect-space line shapes themselves are not known. Limitations for undersample d or highly broadened spectra are discussed, along with extensions to two- or higher-dimensional arrays of data. (C) 2001 American Institute of Physic s.