Signal Processor Inverse Matrix Approximation
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Solution Overview
Problem
Signal processing applications face challenges with ill-conditioned matrices, which existing methods address through regularization, virtual noise, or singular value decomposition, but these approaches often sacrifice performance or complexity.
Innovation Solution
A method using the adjoint of a matrix and a scaling factor associated with its determinant to approximate the inverse matrix, avoiding numerical difficulties and improving performance across various signal processing applications.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional matrix inversion methods (regularization, virtual noise, SVD) are used to handle ill-conditioned matrices, then numerical stability is improved, but performance is sacrificed or complexity increases
Solution Approach 1:
The patent changes the parameter representation by working with the adjoint matrix and determinant directly rather than computing the inverse matrix. This parameter transformation allows handling ill-conditioned matrices through the adjoint-determinant relationship without requiring regularization or SVD decomposition, thereby maintaining both numerical stability and signal processing performance.
2Reliability
If conventional matrix inversion methods are used to handle ill-conditioned matrices, then numerical stability is improved, but device complexity increases
Solution Approach 1:
The patent extracts the essential information needed for matrix inversion by computing only the adjoint matrix and determinant, rather than performing full matrix inversion or SVD decomposition. This extraction approach reduces computational complexity while maintaining numerical stability for ill-conditioned matrices.
3Loss of information
If typical matrix inversion is calculated for ill-conditioned matrices, then complete inverse information is obtained, but numerical difficulties occur
Solution Approach 1:
The patent introduces the adjoint matrix and determinant as intermediary elements that mediate between the ill-conditioned matrix and the desired inverse information. By computing the adjoint and determinant separately and using their relationship, the method avoids direct inversion of ill-conditioned matrices, preventing numerical difficulties while preserving inverse accuracy.
Data Source
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AI summary
A device that estimates information from a signal includes a receiver for receiving an input signal and electronic processing circuitry. The electronic processing circuitry generates a matrix associated with the input signal and determines an approximation of an inverse of the matrix based on the adjoint of the matrix and a scaling factor associated with the determinant of the matrix. This approximation avoids possible mathematical difficulties that may be encountered in certain situations when a typical matrix inversion is calculated. The approximated inverse matrix is applied to the input signal to transform the input signal into an output signal. Information associated with the input signal is then determined based on the output signal.