Comparison of wavelet transform and Fourier self-deconvolution (FSD) and wavelet FSD for curve fitting

The advantages of combining Fourier self-deconvolution (FSD) and wavelet transform with curve fitting for the analysis of severely overlapped bands are compared. It is shown that, for overlapped peaks with lower signal-to-noise ratios (SNR), the method of combined wavelet transform with curve fitting provides significantly better results. In contrast, the method of combined FSD with curve fitting shows better results for severely overlapped peaks with higher SNR. Consequently, when wavelet-FSD, which is based on the combination of wavelet transform and FSD, is used to resolve severely overlapped peaks prior to curve fitting, it is shown that there is a great improvement in the conditioning of curve fitting even for severely overlapped peaks with higher noise levels. Therefore, more accurate peak parameters are achieved.

[1]  D. Kell,et al.  An introduction to wavelet transforms for chemometricians: A time-frequency approach , 1997 .

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

[3]  Bhavik R. Bakshi,et al.  Multiscale analysis and modeling using wavelets , 1999 .

[4]  Steven M. Cramer,et al.  Deconvolution of overlapping chromatographic peaks using a cerebellar model arithmetic computer neural network , 1993 .

[5]  Desire L. Massart,et al.  Noise suppression and signal compression using the wavelet packet transform , 1997 .

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

[7]  P. Griffiths,et al.  Protein Conformation by Infrared Spectroscopy: Resolution Enhancement by Fourier Self-Deconvolution , 1985 .

[8]  Gerrit Kateman,et al.  CURVE-FITTING USING NATURAL COMPUTATION , 1994 .

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

[10]  R. Buck,et al.  Generalized spectral decomposition method applied to infrared, ultraviolet, and atomic emission spectrometry , 1976 .

[11]  W. L. Mead,et al.  The measurement of derivative i.r. spectra—I. Background studies , 1982 .

[12]  James W. McNicol,et al.  The Use of Principal Components in the Analysis of Near-Infrared Spectra , 1985 .

[13]  R. W. Snyder,et al.  A Fourier Transform Infrared Study of Mineral Matter in Coal: The Application of a Least Squares Curve-Fitting Program , 1981 .

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

[15]  J. Koenig,et al.  Least-Squares Curve-Fitting of Fourier Transform Infrared Spectra with Applications to Polymer Systems , 1977 .

[16]  Jianbin Zheng,et al.  Wavelet frequency spectrum analysis of oscillograms , 1999 .

[17]  S P Levine,et al.  Spectral peak verification and recognition using a multilayered neural network. , 1990, Analytical chemistry.

[18]  Peter R. Griffiths,et al.  Comparison of Fourier self-deconvolution and maximum likelihood restoration for curve fitting , 1991 .