Fourier Deconvolution in Non-Self-Deconvolving Conditions. Effective Narrowing, Signal-to-Noise Degradation, and Curve Fitting

The effect of Fourier deconvolution on band narrowing and on the decrease of signal-to-noise ratio has been studied for a generalized case in which the width used in the deconvolution does not match the actual bandwidth. For the identification of underlying component bands, our results show that application of infra-deconvolution (i.e., the bandwidth used for deconvolution is lower than the actual bandwidth) produces a high degradation of the signal-to-noise ratio and poor band narrowing. On the contrary, self- or over-deconvolution, with lower signal-to-noise degradation and higher band narrowing, seem more suitable for this purpose. Relative to quantitative analysis, we rely on both theoretical and practical aspects to propose the generalized use of Voigt band shapes as a fairly correct general model to be used in the curve fitting of deconvoluted bands. With its use, the curve fitting of noise-free deconvoluted bands retrieved the original band parameters with high accuracy. The noise effect on the parameter precision obtained by curve fitting a deconvoluted noisy Lorentzian band was also studied. Finally, the existence of optimum deconvolution parameters for curve fitting complex spectra is considered, and a general recommendation for approaching this optimum is given.

[1]  Douglas J. Moffatt,et al.  A New Line-Narrowing Procedure Based on Fourier Self-Deconvolution, Maximum Entropy, and Linear Prediction , 1991 .

[2]  H. Mantsch,et al.  Noise in Fourier self-deconvolution. , 1981, Applied optics.

[3]  D. Moffatt,et al.  Deconvolution, Derivation, and Smoothing of Spectra Using Fourier Transforms , 1984 .

[4]  Karel Heremans,et al.  How to Minimize Certain Artifacts in Fourier Self-Deconvolution , 1995 .

[5]  E Goormaghtigh,et al.  Secondary structure and dosage of soluble and membrane proteins by attenuated total reflection Fourier-transform infrared spectroscopy on hydrated films. , 1990, European journal of biochemistry.

[6]  A. Barth.  Fine-structure enhancement--assessment of a simple method to resolve overlapping bands in spectra. , 2000, Spectrochimica Acta Part A - Molecular and Biomolecular Spectroscopy.

[7]  W. Hübner,et al.  Fourier Self-Deconvolution: Parameter Determination and Analytical Band Shapes , 1996 .

[8]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[9]  A. Myers.  Molecular electronic spectral broadening in liquids and glasses. , 1998, Annual review of physical chemistry.

[10]  Curve Fitting and Fourier Self-Deconvolution for the Quantitative Representation of Complex Spectra , 1987 .

[11]  P. Griffiths.  Fourier Transform Infrared Spectrometry , 2007 .

[12]  J. Bandekar,et al.  Vibrational spectroscopy and conformation of peptides, polypeptides, and proteins. , 1986, Advances in protein chemistry.

[13]  R. S. Jackson,et al.  Combined deconvolution and curve fitting for quantitative analysis of unresolved spectral bands , 1990 .

[14]  M. Pézolet,et al.  Determination of the secondary structure content of proteins in aqueous solutions from their amide I and amide II infrared bands. Comparison between classical and partial least-squares methods. , 1990, Biochemistry.

[15]  S. Venyaminov,et al.  Quantitative IR spectrophotometry of peptide compounds in water (H2O) solutions. II. Amide absorption bands of polypeptides and fibrous proteins in α‐, β‐, and random coil conformations , 1990, Biopolymers.

[16]  R. Mersereau,et al.  Iterative methods for image deblurring , 1990 .

[17]  D. Oxtoby.  Vibrational Relaxation in Liquids , 1972 .

[18]  A. Marshall,et al.  Time-Domain (Interferogram) and Frequency-Domain (Absorption-Mode and Magnitude-Mode) Noise and Precision in Fourier Transform Spectrometry , 1990 .

[19]  Douglas J. Moffatt,et al.  Fourier Self-Deconvolution: A Method for Resolving Intrinsically Overlapped Bands , 1981 .

[20]  H. Mantsch,et al.  Fourier transforms in the computation of self-deconvoluted and first-order derivative spectra of overlapped band contours , 1981 .

[21]  J. Callis,et al.  Direct Use of Second Derivatives in Curve-Fitting Procedures , 1989 .

[22]  P. Saarinen.  Spectral Line Narrowing by Use of the Theoretical Impulse Response , 1997 .

[23]  D. K. Buslov,et al.  Regularized Method of Spectral Curve Deconvolution , 1997 .

[24]  S. Tatulian,et al.  Infrared spectroscopy of proteins and peptides in lipid bilayers , 1997, Quarterly Reviews of Biophysics.

[25]  H. Susi,et al.  Examination of the secondary structure of proteins by deconvolved FTIR spectra , 1986, Biopolymers.

[26]  Douglas J. Moffatt,et al.  A Generalized Approach to Derivative Spectroscopy , 1987 .

[27]  R. Narayan,et al.  Maximum Entropy Image Restoration in Astronomy , 1986 .

[28]  F. Goñi,et al.  Quantitative studies of the structure of proteins in solution by Fourier-transform infrared spectroscopy. , 1993, Progress in biophysics and molecular biology.