The fast wavelet transform on compact intervals as a tool in chemometrics II. Boundary effects, denoising and compression

This paper addresses a commonly observed problem with applying wavelet tran sforms (WT) to signals from laboratory measurements. These are the boundary effects which occur when analyzing finitely supported signals. The usual m ethods of how to avoid these kind of artefacts are discussed, and a solutio n to the problem is suggested by applying so-called Sturm-Liouville wavelet s (due to one of the present authors). We demonstrate that this type of wav elet can be used for signal denoising with a minimal loss of energy, a prop erty which is well known to classical wavelets; this property also finds ap plications to data compression. All discussed methods are tested on data or iginating from NIR-spectrometric measurements. (C) 1999 Elsevier Science B. V. All rights reserved.