Analyse mathématique de spectres ir par calcul automatique

Comparison of Fourier self-deconvolution and maximum likelihood restoration for curve fitting

“…It was shown that the combination of FSD and subsequent least-squares curve-fitting allowed objective optimization of the parameters used in FSD, assisted in the determination of the number of bands, and significantly improved the mathematical conditioning of the curve-fitting when compared with fitting the original spectrum. This last advantage is perhaps the most significant, since curve-fitting is inherently ill-conditioned and even small errors in the input data or the assumptions can lead to very large errors in the fitted parameters (2)(3)(4)(5)(6). In our initial studies the synthetic spectra used were all noise free; in this paper those studies have been extended to include the effects of noise.…”

“…The inverse Fourier transform of A(v) is N Y(x) = 0.25 7| ,•0 exp(-2irjVi°x) ß (-, ) -0 for |x| < R~l (2) where ; = V(-l), R is the nominal resolution, and x is the spatial frequency. In FSD, Y(x) is multiplied by ß ( ' ), where y' < y, to yield Y'(x): Y'(x) = 0.25 7 A,•0 exp(-2iri/i'i°x) exp[-ir(7¡ -y')x] i=0 for |x| < fi'1 (3) When the forward Fourier transform of Y'(x) is calculated, we obtain A'(V) = £ A hi__(7¿ -7')2 £ (7;-7') (7;-7')2 + 4( -/>)2 (4) 0003-2700/91/0363-2557602.50/0 &copy; 1991 American Chemical Society (This equation has not been simplified, to permit comparison with eq 1.) This "deconvolved" spectrum still has Lorentzian bands in the same positions, but the width of each band has been decreased by an amount y' and the peak absorbance has been increased by the factor y¡/(y¡ -y').…”