Del Análisis de Fourier al Análisis Wavelet

Abstract

The wavelet transform is a relatively recent tool of analysis, developed in different science fields and by different people whose research has been integrated in a formal theory since the eighties. This topic is presented as a transition from the classic Fourier theory towards the new ideas represented by the wavelet transform in the realm of the digital signal processing. By using the Fourier theory as a basis for the development of the wavelet operator, an objective standard is achieved in order to compare the performance of both transformations. The differences and similitudes, advantages, disadvantages are made clear by this approach and, finally, the complementarity of both is established. The new operator does not make obsolete the previous one. In addition, the many applications described show the practical utility and the perspectives of use of both mathematical tools in the different branches of science.