Signal processing of multi-channel data
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.
1. A method for providing linear prediction, the method comprising:
collecting multi-channel data from a plurality of independent sources;
representing the multi-channel data as vectors of quaternions;
generating an autocorrelation matrix corresponding to the quaternions; and
outputting linear prediction coefficients based upon the autocorrelation matrix, wherein the linear prediction coefficients represent a compression of the collected multi-channel data.
2. A method according to claim 1 , wherein the data in the representing step includes at least one of 3-dimensional data and 4-dimensional data.
3. A method according to claim 1 , wherein the multi-channel data represents one of video signals, and voice signals.
4. A method for supporting video compression, the method comprising:
collecting time series video signals as multi-channel data, wherein the multi-channel data is represented as vectors of quaternions;
generating an autocorrelation matrix corresponding to the quaternions; and
outputting linear prediction coefficients based upon the autocorrelation matrix.
5. A method according to claim 4 , further comprising:
transmitting the linear prediction coefficients over a data network to a remote video display for displaying images represented by the video signals that are generated from the transmitted linear prediction coefficients.
6. A method of signal processing, the method comprising:
receiving multi-channel data;
representing multi-channel data as vectors of quaternions; and
performing linear prediction based on the quaternions.
7. A method according to claim 6 , further comprising:
outputting an autocorrelation matrix corresponding to the quaternions, wherein the linear prediction is performed based on the autocorrelation matrix.
8. A method according to claim 6 , wherein the data in the representing step includes at least one of 3-dimensional data and 4-dimensional data.
9. A method according to claim 6 , wherein the multi-channel data represents one of video signals, and voice signals.
10. A method of performing linear prediction, the method comprising:
representing multi-channel data as a pseudo-invertible matrix;
generating a pseudo-inverse of the matrix; and
outputting a plurality of linear prediction weight values and associated residual values based on the generating step.
11. A method according to claim 10 , wherein the multi-channel data is represented as a vector of quaternions.
12. A method according to claim 10 , further comprising:
computing Levinson parameters corresponding to the matrix, wherein the plurality of linear prediction weight values and associated residual values is based on the computed Levinson parameters.
13. A method according to claim 10 , wherein the matrix has scalars that are non-commutative.
14. A method according to claim 10 , wherein the multi-channel data is represented as elements of a random path module.
15. A computer-readable medium carrying one or more sequences of one or more instructions for performing signal processing, the one or more sequences of one or more instructions including instructions which, when executed by one or more processors, cause the one or more processors to perform the steps of:
receiving multi-channel data;
representing multi-channel data as vectors of quaternions; and
performing linear prediction based on the quaternions.
16. A computer-readable medium according to claim 15 , wherein the one or more processors further perform the step of:
outputting an autocorrelation matrix corresponding to the quaternions, wherein the linear prediction is performed based on the autocorrelation matrix.
17. A computer-readable medium according to claim 15 , wherein the data in the representing step includes at least one of 3-dimensional data and 4-dimensional data.
18. A computer-readable medium according to claim 15 , wherein the multi-channel data represents one of video signals, and voice signals.
19. A computer-readable medium carrying one or more sequences of one or more instructions for performing linear prediction, the one or more sequences of one or more instructions including instructions which, when executed by one or more processors, cause the one or more processors to perform the steps of:
representing multi-channel data as a pseudo-invertible matrix;
generating a pseudo-inverse of the matrix; and
outputting a plurality of linear prediction weight values and associated residual values based on the generating step.
20. A computer-readable medium according to claim 19 , wherein the multi-channel data is represented as a vector of quaternions.
21. A computer-readable medium according to claim 19 , wherein the one or more processors further perform the step of:
computing Levinson parameters corresponding to the matrix, wherein the plurality of linear prediction weight values and associated residual values is based on the computed Levinson parameters.
22. A computer-readable medium according to claim 19 , wherein the matrix has scalars that are non-commutative.
23. A computer-readable medium according to claim 19 , wherein the multi-channel data is represented as elements of a random path module.