The analytical solution of gamma filter model

Gamma filter has been proposed by De Vries and Principe (1992) as a functional approximator. In order to get the (sub) optimal values of weights and (temporal resolution) μ, numerical training algorithms have been derived by Lawrence et al. (1996) and Principe et al. (1994). This paper presents an analytical approach to this optimization problem. Using the classical Laguerre polynomial, we have successfully uncoupled and derived the optimal exact solutions for the weights and μ. Finally, we have a geometrical interpretation of the whole idea as an inner product preserved transformation between linear vector spaces