Error Analysis of Padding Schemes for DFT's of Convolutions and Derivatives.

摘要

Various padding schemes have been proposed in the geodetic literature to avoid the error committed by approximating a linear convolution with a cyclic convolution; the latter is needed to implement Fast Fourier transform techniques. The method of extending the signal with zeros and the kernel with its own values yields equality between the two types of convolutions. However, it is shown using error transfer functions and numerical examples that the cyclic convolution error is not greater than the edge effect. Since the edge effect must be avoided in any case, there is justification for dispensing with the padding of arrays that adds considerably to computer memory requirements. The analysis is extended to the method of properly defined discrete, derivative operator transforms where the corresponding cyclic convolution error is confined to computation points very close to the edge.