| In this project problems related to wavelet applications are studied. An analysis of the behaviour of a chain of decimators when its input is white Gaussian noise on the assumption of finite duration input signals is presented. A structure for the output correlation matrix of the system is obtained. In addition, an upper and lower bound for the unitary norms of the output correlation matrix are given. These bounds will provide information about the inverse of the output correlation matrix with respect to its condition number. After this characterization is done, the creation of a positive wavelet projection into wavelet subspaces to represent positive signals is shown. The positive wavelet projections are based on the creation of positive kernels as shown by Walter [1]. This theory is applied and simplified in order to obtain computationally feasible positive projections which can be applied in real life applications. Finally, an application where a positive wavelet projection is used to improve the computational speed of a QR factorization algorithm is showed. |
