Geometrical characterization of the canonical coordinate basis underlying a family of error minimizing signal compression techniques

A geometrical interpretation is used to illustrate the interrelationships that exist between autoregressive analysis, principal component analysis, and certain canonical coordinate-based non-euclidean error minimization procedures. The generalized eigenvector approach to these error minimization problems has a geometrical characterization, in N-space, that provides insight into their performance. This applies to the error bound interrelationships that exist between these signal representation procedures and also to the stability of the error minimizing transformation coefficients obtained from the different procedures. The geometrical interpretation also provides insight into the effects of eigenvalue degeneracy in introducing ambiguities into the analysis coefficient determination process.