The gradient of a sampled function†
M. MOR · International Journal of Control · 1970
One of the applications of digital computers in processing sampled data is in determining the gradient of a sampled function. In this paper an algorithm is found for determining the gradient in N dimensions of an N-dimensional wave-number-limited function from its samples. The gradient is found at the sampling points. An upper bound to the truncation error is calculated. The dependence of this error on the pitch of the sampling lattice, the number of samples and the maximum exeursion is found for a cardinal reconstruction function.