On the determination of the optimal center and scale factor for truncated Hermite series

Signals that are fairly concentrated in time or space can often be conveniently described by a truncated Hermite series. The rate of convergence of such series depends on the center and scale factor of the Hermite functions. In this paper we present some results concerning the determination of the optimal values of these two important parameters. We address the problem of the approximation of one-dimensional functions defined in the continuous interval (−∞,∞).