Análisis de señales utilizando wavelets

This document is an introduction to the Wavelet Theory. The approach given to this research was that the reader be able to appreciate the features that make of wavelets an alternative too for signal analysis. An introduction to the families of wavelets Haar & Daubechie together with the basic concepts for their application are presented. Emphasis is made on a signal processing application in a manufacturing process getting the benefit of one of the most interesting wavelets features which is the localization identification of fast oscilations within a signal. A solution proposal is presented using morphological algorithms in order to compare it with the benefits that can be obtained when using wavelets to the same case study. Both Scaling Functions and Wavelets are presented and also the procedure to obtain the Wavelets Functions from the corresponding Scaling Functions. Mathematical basis are studied as an illustration perspective rather than rigorous demonstrations because the purpose of the present document was to be a didactic guide which will provide an introduction to the wavelets concepts to future students interested in this field and above al an easy understanding of the wavelet properties in order to be able to apply them on Signal Processing tasks. Al of the code by all the different algorithms for the transformations using both wavelets Haar & Daubechie was developed in Mathematica and the source files are available on both the appendix and on the attached CD.