Signal processing using the generalized Taylor series expansion

A new orthonormal basis function, called the generalized Taylor series expansion is presented. The authors show that the expansion is obtainable for a large class of functions. The expansion is performed about another function rather than a point, which is the case of ordinary Taylor series. The root function can be tailored to be similar to the desired function. The dilated and translated version of a signal can also be expanded. Finally, this expansion is used in an adaptive signal or function identification scheme