An approach for providing non-commutative approaches to signal processing. Quaternions are used to represent multi-dimensional data (e.g., three- and four-dimensional data). Additionally, a linear predictive coding scheme (e.g., based on the Levinson algorithm) that can be applied to wide class of signals in which the autocorrelation matrices are not invertible and in which the underlying arithmetic is not commutative. That is, the linear predictive coding scheme multi-channel can handle singular autocorrelations, both in the commutative and non-commutative cases. This approach also utilizes random path modules to replace the statistical basis of linear prediction.