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For the continuous Fourier transform, the set of basis functions is
defined by
| |
(18) |

where is the continuous frequency. For a 1-point
sampling interval, the frequency is limited by the Nyquist
condition: . In this case, the interpolation
function *W* can be computed from formula (13) to be
| |
(19) |

The interpolation function (19) is well-known as the
Shannon sinc interpolator. A known problem with its practical
implementation is the slow decay with (*x* - *n*). This problem is
solved in practice with heuristic tapering Hale (1980),
such as Harlan's triangle tapering Harlan (1982). While
the function *W* from equation (19) automatically
satisfies properties (3) and (17), where
both *x* and *n* range from to , its tapered
version may require additional normalization.

** Next:** Discrete Fourier basis
** Up:** Interpolation with Fourier basis
** Previous:** Interpolation with Fourier basis
Stanford Exploration Project

11/11/1997