Method and system for rapid identification of multiple input systems
View Patent ↗The disclosure describes techniques for determining the response characteristics of a system. One such technique includes applying a series of M vector probe input signal sets of a form {overscore (V)} m x(t) to the system, wherein {overscore (V)} m is an m-th column of a matrix V and x(t) is a scalar input signal. The response signals {overscore (y)} t are measured and a single-input system {overscore (F)} m (z) is determined by considering the approximate relationship {overscore (y)} z ≈{overscore (F)} m (z)x(z), where {overscore (F)} m (z) is an m-th column of a matrix F(z). The system characteristics can be determined from the relationship H(z)=F(z)V −1 , where V −1 denotes the right-matrix-inverse of the matrix V. The matrix V may be a matrix with mutually orthogonal rows, or may have entries consisting of plus one and minus one values, or may be a portion of a Hadamard matrix.
1. A method of determining characteristics of a system H(z) having multiple inputs, the method comprising:
applying to the system a series of vector probe input signal sets, each vector probe input signal set being formed using a column of a matrix V and a scalar input signal;
measuring a response signal of the system;
determining a single-input system {overscore (F)} m (z) by considering an approximate relationship where a z-transform of the scalar input signal applied to the single-input system yields a z-transform of the response signal of the system;
determining a multiple-input system F(z) as the system whose m-th column is the determined single-input system {overscore (F)} m (z);
obtaining a right-matrix-inverse of the matrix V; and
multiplying the multiple-input system F(z) by the right-matrix-inverse of the matrix V to determine the characteristics of the system H(z).
2. The method of claim 1 , comprising choosing rows of the matrix V to be mutually orthogonal.
3. The method of claim 1 , comprising choosing entries in the matrix V to consist of plus one and minus one values.
4. The method of claim 3 , comprising choosing rows of the matrix V to be mutually orthogonal.
5. The method of claim 4 , wherein choosing the matrix V comprises choosing the matrix V as N rows of a Hadamard matrix with dimension M×M, where N is the number of multiple input signals of the system and M≧N.
6. The method of claim 5 , wherein choosing the matrix V comprises choosing M as a whole number power of 2.
7. The method of claim 6 , wherein determining the system characteristics comprises using a Fast Hadamard Transformation.
8. The method of claim 6 , wherein determining the single-input system comprises:
correlating the input signals with themselves and with the output signals to obtain a set of normal equations; and
solving the set of normal equations.
9. The method of claim 8 , wherein solving comprises using a technique taken from a list of techniques comprising a Cholesky decomposition method and a preconditioned conjugate gradient method.
10. The system of claim 9 , wherein determining the system characteristics comprises using a Fast Hadamard Transformation.
11. The system of claim 1 , wherein determining the system characteristics comprises using a Fast Hadamard Transformation.
12. The method of claim 1 , wherein determining the single-input system comprises:
correlating the input signals with themselves and with the output signals to obtain a set of normal equations; and
solving the set of normal equations.
13. The method of claim 12 , wherein solving comprises using a technique taken from a list of techniques comprising a Cholesky decomposition method and a preconditioned conjugate gradient method.
14. A computer program, disposed on a computer readable medium, for determining characteristics of a system H(z) having multiple inputs, the computer program including instructions for causing a processor to:
apply to the system a series of vector probe input signal sets, each vector probe input signal set being formed using a column of a matrix V and a scalar input signal;
measure a response signal of the system;
determine a single-input system {overscore (F)} m (z) by considering an approximate relationship where a z-transform of the scalar input signal applied to the single-input system yields a z-transform of the response signal of the system;
determine a multiple-input system F(z) as the system whose m-th column is the determined single-input system {overscore (F)} m (z);
obtain a right-matrix-inverse of the matrix V; and
multiply the multiple-input system F(z) by the right-matrix-inverse of the matrix V to determine the characteristics of the system H(z).
15. The computer program of claim 14 , wherein the computer program includes instructions for causing the processor to choose entries in the matrix V to consist of plus one and minus one values.
16. The computer program of claim 15 , wherein the computer program includes instructions for causing the processor to choose rows of the matrix V to be mutually orthogonal.
17. The computer program of claim 16 , wherein the computer program includes instructions for causing the processor to choose the matrix V as N rows of a Hadamard matrix with dimension M×M, where N is the number of multiple input signals of the system and M≧N.
18. The computer program of claim 17 , wherein the computer program includes instructions for causing the processor to choose M as a whole number power of 2.
19. The computer program of claim 18 , wherein the computer program includes instructions for causing the processor to determine the system characteristics using a Fast Hadamard Transformation.
20. The computer program of claim 19 , wherein the computer program includes instructions for causing the processor to:
correlate the input signals with themselves and with the output signals to obtain a set of normal equations; and
solve the set of normal equations.
21. The computer program of claim 20 , wherein the computer program includes instructions for causing the processor to use a technique for solving the set of normal equations taken from a list of techniques comprising a Cholesky decomposition method and a preconditioned conjugate gradient method.
22. A system for determining characteristics of a multiple input system H(z), the system comprising:
means for applying to the system a series of vector probe input signal sets, each vector probe input signal set being formed using a column of a matrix V and a scalar input signal;
means for measuring a response signal of the system;
means for determining a single-input system {overscore (F)} m (z) by considering an approximate relationship where a z-transform of the scalar input signal applied to the single-input system yields a z-transform of the response signal of the system;
means for determining a multiple-input system F(z) as the system whose m-th column is the determined single-input system {overscore (F)} m (z);
means for obtaining a right-matrix-inverse of the matrix V; and
means for multiplying the multiple-input system F(z) by the right-matrix-inverse of the matrix V to determine the characteristics of the system H(z).