Smooth Extension of Functions Known at Discrete Points--Application to Magnetic Signature Measurements.

摘要

Magnetic signature measurements of tanks at Aberdeen, MD, are taken that effectively measure the vertical field in a plane below the tank at points spaced 1 ft apart in a 20 x 40 ft grid. By use of a discrete Fourier series expansion, the measurements A(pq) are extended to arbitrary points within the area by R(uv) where R(pq) = A(pq) for integer p,q. This extension allows one to compare sets of measurements that are slightly shifted with respect to one another. Formulas are given by which one may calculate these shifts explicitly if they are assumed small, as well as obtain them by minimizing the square deviation between two functions for arbitrary shifts. (Author)