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 transforms (WT) to signals from laboratory measurements. These are the boundary effects which occur when analyzing finitely supported signals. The usual methods of how to avoid these kind of artefacts are discussed, and a solution to the problem is suggested by applying so-called Sturm–Liouville wavelets (due to one of the present authors). We demonstrate that this type of wavelet can be used for signal denoising with a minimal loss of energy, a property which is well known to classical wavelets; this property also finds applications to data compression. All discussed methods are tested on data originating from NIR-spectrometric measurements.