Abstract: 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.

Abstract: A wireless communication system and method for determining a location of a mobile station communicating within the system. The system comprises a plurality of base receivers for receiving wireless communication, a controller, and at least one mobile station for transmitting a signal for receipt by at least two of the base receivers. The base receivers that received the transmitted signal determine a timing error associated with the transmitted signal, and the controller determines a separation distance between the mobile station and each base receiver that received the transmitted signal based at least upon the timing error. The controller further determines the location of the mobile station within the wireless communication network based upon the separation distance between the mobile station and the base receivers that received the transmitted signal.

Abstract: 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.