An efficient frequency-domain algorithm for discrete orthogonal basis restoration

Discrete orthogonal basis restoration (DOBR) is a robust method for the inverse solution of linear systems of the type [A][o]=(i), where [A] may be either shift variant or invariant. Presented in this work is the derivation of a frequency-domain DOBR algorithm that significantly improves computational efficiency. Substantial reductions in the number of arithmetic operations are possible when system stationarity allows the use of precalculated DOBR characteristic vector sets, and sampling of the signal is rapid relative to the highest frequency of interest. More modest improvements in computational efficiency (10%-40%) are obtained when the entire DOBR algorithm must be executed. In addition to reducing the number of floating-point operations and storage requirements, the frequency-domain DOBR algorithm lessens the deleterious effects of perturbations in [A] on the inverse solution.