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US 10,951,919 B2Granted
Multivariable matrix spectral factorization
AssigneeNew York University in Abu Dhabi Corporation
InventorsLasha Ephremidze, Ilya Spitkovsky
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Abstract
A method for performing Multivariable Matrix Spectral Factorization has been developed, which allows factorization in real time high-dimensional matrices with multivariable high-order polynomial or non-rational entries. Systems implementing the method provide improved performance and capabilities in applications reducible to multivariable matrix spectral factorization.
Claims20
A computer system comprising
- a receiver for receiving multidimensional information;
- one or more processors;
- and
- a non-transitory computer-readable medium operatively connected to the one or more processors and including computer code configured to:
- receive a signal input based upon n parameters, where n is greater than 1;
- apply n-D Matrix Spectral Factorization to the received signal input;
- and
- transmit an output of the n-D Matrix Spectral Factorization;
- and
- wherein the n-D Matrix Spectral Factorization is a multivariable matrix spectral factorization comprising:
- performing, for a given multivariable matrix spectral density, a lower-upper triangular factorization to factor the given multivariable matrix spectral density into a first matrix and a conjugate transpose of the first matrix, and
- recurrently processing the first matrix by preparing an auxiliary matrix considering a submatrix of the first matrix, expanding auxiliary entries of the auxiliary matrix into series with general coefficients, cutting the tails, constructing multivariable 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.
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An apparatus, comprising:
- receiving means for receiving a signal input based upon n parameters, where n is greater than 1;
- processing means for applying n-D Matrix Factorization to the received signal input;
- and
- transmitting means for providing a signal output of the n-D Matrix Spectral Factorization;
- and
- wherein the n-D Matrix Spectral Factorization is a multivariable matrix spectral factorization comprising:
- performing, for a given multivariable matrix spectral density, a lower-upper triangular factorization to factor the given multivariable matrix spectral density into a first matrix and a conjugate transpose of the first matrix, and
- recurrently processing the first matrix by preparing an auxiliary matrix considering a submatrix of the first matrix, expanding auxiliary entries of the auxiliary matrix into series with general coefficients, cutting the tails, constructing multivariable 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.
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A method executing on one or more processors, comprising:
- receiving a signal input based upon n parameters, where n is greater than 1;
- applying n-D Matrix Spectral Factorization to the received signal input by:
- performing, for a given multivariable matrix spectral density, a lower-upper triangular factorization to factor the given multivariable 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, expanding auxiliary entries into series with general coefficients, cutting the tails, constructing multivariable 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;
- and
- transmitting an output of the n-D Matrix Spectral Factorization.
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Dependencies are inferred from the claim text.