A speech waveform analysis and reconstruction process based on non-euclidean error minimization and matrix array procesing techniques

This paper describes the implementation of a matrix array processor oriented technique that can transform time sampled speech waveform data, by way of the frequency domain, into a psendo-canonical coordinate domain whose components can be ordered in such a manner as to commit the smallest signal reconstruction error, relative to a given non-euclidean quadratic error criterion, when certain ordered components are not used in the reconstruction process. The error metric can be specified, in either the time or frequency domain, in the form of a complex valued hermitian matrix, thus allowing a very large number of degrees of freedom that can be used to incorporate certain statistical, dynamical and psychoacoustic attributes of the speech data into the analysis and reconstruction process. For the case of a simple euclidean error metric, the pseudo-canonical coordinate process is shown to reduce to the well known principal component, or Loevé-Karhunen, signal representation technique.