Abstract: The present invention relates to a novel matrix-valued transform framework to process digital signals. According to one aspect of the invention, matrix-valued methods and apparatus are described to transform a vector-valued discrete-time data sequence from time-domain into frequency-domain. In another aspect, matrix-valued methods and apparatus are described to transform a vector-valued data sequence from frequency-domain into time-domain. Furthermore, the new framework disclosed in this invention also provides a plurality of methods and apparatus for basic signal processing functions and operations of a matrix-valued communication system. These functions and operations include but are not limited to matrix-valued fast Fourier transformation, matrix-valued linear and circular convolution, matrix-valued correlation, matrix-valued multiplexing and de-multiplexing, and matrix-valued data coding and decoding.

Abstract: The present invention relates to a novel matrix-valued transform framework to process digital signals. According to one aspect of the invention, matrix-valued methods and apparatus are described to transform a vector-valued discrete-time data sequence from time-domain into frequency-domain. In another aspect, matrix-valued methods and apparatus are described to transform a vector-valued data sequence from frequency-domain into time-domain. Furthermore, the new framework disclosed in this invention also provides a plurality of methods and apparatus for basic signal processing functions and operations of a matrix-valued communication system. These functions and operations include but are not limited to matrix-valued fast Fourier transformation, matrix-valued linear and circular convolution, matrix-valued correlation, matrix-valued multiplexing and de-multiplexing, and matrix-valued data coding and decoding.