Modelling 1-D signals using Hermite basis functions

The paper discusses a method for estimating the Hermite coefficients of a discrete-time one-dimensional signal. To estimate the Hermite coefficients a solution based on Gaussian quadratures is used. The paper also looks at various least mean squared (LMS) estimation methods to estimate two further parameters which are incorporated into the orthonormal Hermite basis function; a spread term and a shift term. In addition, the effects of scaling, dilation and translates of a signal on its Hermite coefficients, spread and shift terms are presented. The paper concludes with a brief discussion on the potential application of the Hermite parameters as features for use in problems requiring shape discrimination within a one-dimensional signal. It also mentions those applications where this was found to be appropriate