Signal compression model interrelationships in the time, frequency, principal component and canonical coordinate domains

This paper describes the use of a canonical signal compression and modelling technique that permits the minimization of certain non-euclidean types of signal resynthesis error criteria. The technique is based on the construction of a non-orthogonal transformation from the original sampled signal representation, in either the time, frequency or spatial domain, to a special canonical coordinate domain. The parameters characterizing this transformation are then chosen to minimize the specified error criterion, for each level of truncation of the canonical coordinate based signal representation. A mechanism for factoring this canonical coordinate transformation into an eigenvector-eigenvalue based correlation simplification process and an error metric simplification process, is described. This mechanism is shown to involve principal component (or Loeve-Karhunen) analysis as an intermediate step in the complete canonical coordinate determination process, and can lead to a substantial simplification in the computational complexity that is entailed in handling a class of non-euclidean error criteria.