Simultaneous extrapolation in time and frequency domains using hermite expansions

The time-domain response of a three-dimensional (3-D) conducting object is: modeled as an associate hermits (AH) series expansion. Using the isomorphism of the AH function and its Fourier transform, the frequency-domain response can be expressed as a scaled version of the time-domain expansion. Using early-time and low-frequency data, we demonstrate simultaneous expansion in both domains; This approach is attractive because expansions with only 10-20 terms give good extrapolation in both time and frequency domains. The computation involved is minimal with this method.