Functional transformation of Fourier-transform mid-infrared spectrum for improving spectral specificity by simple algorithm based on wavelet-like functions

Herein a simple algorithm for the mathematical transformation of FTIR spectrum was developed, evaluated, and applied for description of different systems. Water, ethanol, n-butanol, n-hexanol, formic acid, acetic acid, citric acid, and water-acetic acid mixtures at different concentrations were used as model systems. We found that functional transformation of FTIR spectrum can be performed by functionally-enhanced derivative spectroscopy approach using the Function P, which is defined as P = (1 + aj )(s)-0.5 where aj and s are the absorbance and the scale factor, respectively. It is also demonstrated that Function P can be used for qualitative and quantitative analysis of pure substances and mixtures. It is concluded that Function P can be understood as a wavelet transformation, which is evaluated at small times and displacements, with scaling factor given by the change of absorbance inverse.