Wavelet Transform: A Method for Derivative Calculation in Analytical Chemistry

Abstract

A novel method based on wavelet transform is proposed in this work for approximate derivative calculation. An approximate first derivative of an analytical signal can be expressed as the difference between the two scale coefficients C1, which were generated from any two Daubechies wavelet functions. The optimal results for both synthetic and experimental data were obtained with the use of the Daubechies wavelet functions D8 and D18. Our work demonstrated that the new method can enhance the signal-to-noise ratio at higher order derivative calculation and retain all major properties of the conventional methods.