Principles and applications of wavelet transformation to chemometrics

This paper aims at serving two purposes: firstly, it gives a quick summary of aspects and properties of wavelets and wavelet transforms which are needed in order to understand how to (pre-)process data from spectrometry with wavelet methods. Secondly, it shows on a typical example (wheat NIR spectra) how wavelet transforms can be used in order to extract quantitative information. In contrast to other approaches in the literature, we use special types of wavelets which allow analysing finitely extended signals without introducing artifacts near the boundaries, and we introduce a new way of wavelet coefficient regression in order to build our chemometrical models.