Tailored orthonormal sets for expansion of specific classes of functions

A new class of orthonormal basis functions is defined which is derived from a generalized Taylor series expansion about a function rather than about a point. The basis functions described are thus 'tailored' to the type of signal expected and are particularly useful in expanding scaled and translated functions of specific classes of signals. The expansion is shown to be different from both the wavelet and Gabor transforms, yet maintains the flavor of both. Several examples are presented, including the Gaussian, exponential, and cosine based root functions.< >