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 hermite (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.