Generalized orthogonalization method for finite discrete signals and its application

The problem of finding a pair of biorthogonal functions for the case of finite and discrete signals is considered. Starting from two initial functions which are not necessarily biorthogonal, a general procedure to construct biorthogonal ones is given. Compared to previous orthogonalization methods, this method is more general, flexible and also more systematic. Numerical results are also given to see how different parameters can result in different orthogonalized functions.