Wavelets: teoria i aplicacions al tractament de senyals

Abstract

[en] The present work is aimed to investigate the Wavelets. They may be argued to appear for the first time at the beginning of the 20th century, when Alfréd Haar presented what is currently known as Haar’s base, which will be covered in the third chapter. However, the Wavelets as we know them do not appear until the eighties, when Pierre Goupillaud, Alex Grosman and Jean Morlet carry out the first study using the current terminology. After that, Jan Olov-Strömberg investigated the discrete case, and further important insights were posed by mathematicians such as Ingrid Daubechies and Yves Meyer, who will be mentioned in chapter four. One of the main sources of inspiration to choose this work was the diversity of applications which this theory has displayed both in engineering and computing areas (i.e. the application of the discrete case), and in many physics areas, where it is substituting Fourier’s transform due to its affordances concerning the analysis of time and frequency signal. Furthermore, Wavelets become an essential signals compression tool, as it will be suggested in chapter five.