Optimality condition for truncated generalized Laguerre networks

The optimality condition for the free parameter in a truncated Laguerre network in both continuous-time and discrete-time has recently been established. This condition is of a very simple form and is independent of the power spectrum of the input signal, which makes it attractive for system identification purposes. the simple form of the optimality condition stems from the following property. the derivative of a basis function in the Laguerre series w.r.t. to the free parameter can be expressed in the previous and next basis functions. This property not only applies to the basis functions in a Laguerre series but also to those in specific generalizations of the Laguerre series. In particular we consider the generalized Laguerre functions and what will be called the Meixner-like functions. For these generalizations the same optimality condition as for a Laguerre series holds.