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US 9,318,232 B2Granted
Matrix spectral factorization for data compression, filtering, wireless communications, and radar systems
AssigneeUniversity of Maryland
InventorsAnthony Ephremides, Gigla Janashia, Lasha Ephremidze, Edem Lagvilava
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Abstract
A new apparatus, system, and technique for performing Matrix Spectral Factorization has been developed, which can factorize in real time high-dimensional matrices with high-order polynomial or non-rational entries. The method can be used for efficient implementation of engineering solutions to problems in Data Compression, Filtering, Wireless Communications, and Radar Systems, etc., which are computationally reducible to matrix spectral factorization.
Claims12
An apparatus, comprising:
- a receiver configured to receive a signal input;
- a processor configured to perform Wiener filtering on the received signal even when the received signal is describable with a multi-dimensional matrix with up to infinite order polynomial or non-rational entries;
- and
- a transmitter configured to provide a real-time output of the filtering,
- wherein the Wiener filtering employs matrix spectral factorization, and
- wherein the matrix spectral factorization comprises
- performing, for a given matrix spectral density, a lower-upper triangular factorization to factor the given matrix spectral density into a first matrix and a conjugate transpose of the first matrix,
- recurrently processing the first matrix by preparing an auxiliary matrix considering a submatrix of the first matrix, cutting the tails, constructing wavelet matrices, and increasing a dimension of the considered submatrix, and
- applying a canonical spectral factor to a result of the recurrent processing of the first matrix.
6 more elements
An apparatus, comprising:
- receiving means for receiving a signal input;
- processing means for performing Wiener filtering on the received signal even when the received signal is describable with a multi-dimensional matrix with up to infinite order polynomial or non-rational entries;
- and
- transmitting means for providing a real-time output of the filtering,
- wherein the Wiener filtering employs matrix spectral factorization, and
- wherein the matrix spectral factorization comprises
- performing, for a given matrix spectral density, a lower-upper triangular factorization to factor the given matrix spectral density into a first matrix and a conjugate transpose of the first matrix,
- recurrently processing the first matrix by preparing an auxiliary matrix considering a submatrix of the first matrix, cutting the tails, constructing wavelet matrices, and increasing a dimension of the considered submatrix, and
- applying a canonical spectral factor to a result of the recurrent processing of the first matrix.
6 more elements
A method, comprising:
- receiving a signal input at a computer;
- performing, by the computer, Wiener filtering on the received signal even when the received signal is describable with a multi-dimensional matrix with up to infinite order polynomial or non-rational entries;
- and
- providing, by the computer, a real-time output of the filtering,
- wherein the Wiener filtering employs matrix spectral factorization, and
- wherein the matrix spectral factorization comprises
- performing, for a given matrix spectral density, a lower-upper triangular factorization to factor the given matrix spectral density into a first matrix and a conjugate transpose of the first matrix,
- recurrently processing the first matrix by preparing an auxiliary matrix considering a submatrix of the first matrix, cutting the tails, constructing wavelet matrices, and increasing a dimension of the considered submatrix, and
- applying a canonical spectral factor to a result of the recurrent processing of the first matrix.
6 more elements
A non-transitory computer-readable medium encoded with instructions that, when executed on a computing device perform a process, the process comprising:
- receiving a signal input;
- performing Wiener filtering on the received signal even when the received signal is describable with a multi-dimensional matrix with up to infinite order polynomial or non-rational entries;
- and
- providing a real-time output of the filtering,
- wherein the Wiener filtering employs matrix spectral factorization, and
- wherein the matrix spectral factorization comprises
- performing, for a given matrix spectral density a lower-upper triangular factorization to factor the given matrix spectral density into a first matrix and a conjugate transpose of the first matrix,
- recurrently the first matrix by preparing an auxiliary matrix considering a submatrix of the first matrix, cutting the tails, constructing wavelet matrices and increasing a dimension of the considered submatrix, and
- applying a canonical spectral factor to a result of the recurrent processing of the first matrix.
6 more elements
Dependencies are inferred from the claim text.