Importance of digital processing of signals and images in various fields requires their presentation in adequate form. In this context, various analysis methods exist but the problem was how to choose the best one. in this framework, We tried to present some general analysis methods and to concentrate on the best, wavelet analyze, because its performance and to give a skeletal wavelet example, Beta wavelet, which presents best performances for specifies application like images compression .

carried out Tasks :

- Studing of Beta wavelets : orthogonal and biorthogonal wavelets theory, scales functions, null moment, regularity, translation, dilatation, synthesis analysis filters, ...

- Synthesis of Beta wavelet filters.

- Performance comparation of Beta wavelets filters and DAUBECHIES wavelets for compression application.