Inverse control system
First Claim
1. An inverse control system for an n-input m-output (m being 1 or a greater integer, n being an integer greater than m) linear finite impulse response (FIR) system defining n·
- m signal transmission channels between n input points and m output points, with n transmitting elements being disposed at the respective n input points for providing signals to said linear FIR system, whereinsaid inverse control system is disposed between said n transmitting elements and a common signal source for effecting an inverse control such as to provide desired impulse responses between said signal source and said m output points;
said inverse control system comprises n FIR filters disposed between said signal source and respective said n transmitting elements;
a j-th (j=1, 2, . . . , n) one of said FIR filters connected to a j-th one of said input points through an associated one of said transmitting elements has a number Li of taps which satisfies relationships represented by ##EQU25## for all i=1, 2, . . . , m and j=1, 2, . . . , n where wij is the number of discrete signals representing the impulse response gij (k) of said signal transmission channel between said j-th input point and an i-th (i=1, 2, . . . , m) one of said m output points of said linear FIR system and Pi is the number of discrete signals representing said desired impulse response ri (k) between said signal source and said i-th output point; and
said j-th FIR filter having filter coefficients hj (k) (j=1, 2, . . . , n) satisfying a relationship ##EQU26## for all i=1, 2, . . . , m where ○
* represents a discrete convolution.
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Abstract
An inverse control system is disclosed, which comprises FIR filters provided between transmitting elements at n (n=2, 3, . . . ) input points of a linear FIR system and a common signal source, for an inverse control such as to provide desired impulse responses between the signal source and m (n>m) output points of the linear FIR system. A j-th (j=1, 2, . . . , n) one of the FIR filters has a number Lj of taps which satisfies the relationships represented by ##EQU1## for all i=1, 2, . . . , m and j=1, 2 . . . , n where wij is the number of discrete signals representing the impulse response gij (k) between the j-th output point and i-output point and Pi is the number of discrete signals representing the desired impulse response ri (k) between the signal source and i-th output point. The j-th FIR filters has a filter coefficient hj (k) satisfying the relationship ##EQU2## where ○* is a discrete convolution.
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Citations
25 Claims
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1. An inverse control system for an n-input m-output (m being 1 or a greater integer, n being an integer greater than m) linear finite impulse response (FIR) system defining n·
- m signal transmission channels between n input points and m output points, with n transmitting elements being disposed at the respective n input points for providing signals to said linear FIR system, wherein
said inverse control system is disposed between said n transmitting elements and a common signal source for effecting an inverse control such as to provide desired impulse responses between said signal source and said m output points; said inverse control system comprises n FIR filters disposed between said signal source and respective said n transmitting elements; a j-th (j=1, 2, . . . , n) one of said FIR filters connected to a j-th one of said input points through an associated one of said transmitting elements has a number Li of taps which satisfies relationships represented by ##EQU25## for all i=1, 2, . . . , m and j=1, 2, . . . , n where wij is the number of discrete signals representing the impulse response gij (k) of said signal transmission channel between said j-th input point and an i-th (i=1, 2, . . . , m) one of said m output points of said linear FIR system and Pi is the number of discrete signals representing said desired impulse response ri (k) between said signal source and said i-th output point; and said j-th FIR filter having filter coefficients hj (k) (j=1, 2, . . . , n) satisfying a relationship ##EQU26## for all i=1, 2, . . . , m where ○
* represents a discrete convolution. - View Dependent Claims (3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23)
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4. The inverse control system according to claim 1 or 2, wherein
n=m+1. -
5. The inverse control system according to claim 3, wherein
n=m+1. -
6. The inverse control system according to claim 1 or 2, which further comprises coefficients setting means for computing the filter coefficients hj (k) (j=1, 2, . . . , n) satisfying the relationships (1a), (1b) and (2) by utilizing said impulse response gij (k) and desired impulse response ri (k) and setting the computed filter coefficients hj (k) (j=1, 2, . . . , n) for said j-th FIR filter.
- 7. The inverse control system according to claim 6, wherein representing the relationship (2) by an expression
- space="preserve" listing-type="equation">R=G·
H
said coefficients setting means computes the filter coefficients hj (k) (j=1, 2, . . . , n) using a relationship
space="preserve" listing-type="equation">H=G.sup.T (G·
G.sup.T).sup.-1 ·
Rwhere ##EQU30## - space="preserve" listing-type="equation">R=G·
- m signal transmission channels between n input points and m output points, with n transmitting elements being disposed at the respective n input points for providing signals to said linear FIR system, wherein
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8. The inverse control system according to claim 3, which further comprises coefficients setting means for computing the filter coefficients hj (k) satisfying the relations (2), (3) and (4) by utilizing said impulse response gij (k) and desired impulse response ri (k) and setting the computed filter coefficients hj (k) (j=1, 2, . . . , n) for said j-th FIR filter.
- 9. The inverse control system according to claim 8, wherein representing the relationship (2) by an expression
- space="preserve" listing-type="equation">R=G·
H
said coefficients setting means computes the filter coefficients hj (k) using a relationship
space="preserve" listing-type="equation">H=G.sup.T (G·
G.sup.T).sup.-1 ·
Rwhere ##EQU31## - space="preserve" listing-type="equation">R=G·
- space="preserve" listing-type="equation">R=G·
H
space="preserve" listing-type="equation">H=G.sup.-1 ·
R
- space="preserve" listing-type="equation">R=G·
H
space="preserve" listing-type="equation">H(q+1)=H(q)+α
(q)·
G.sup.T ·
(R-G·
H(q)) (5)
(q) is a step size indicating an amount by which to move from H(q), and ##EQU33##
- space="preserve" listing-type="equation">R=G·
H
space="preserve" listing-type="equation">H=(q+1)=H(q)+α
(q)·
G.sup.T (R=G·
H(q)) (6)
(q) is a step size indicating an amount by which to move from H(q), and ##EQU34##
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2. An inverse control system for an m-input n-output (m being 1 or greater integer, n being an integer greater than m) linear finite impulse response (FIR) system defining m·
- n signal transmission channels between m input points and n output points, with n receiving elements being disposed at the respective n output points for receiving signals provided to said linear FIR system, wherein
said inverse control system is disposed between said n receiving elements and n input terminals of adder means for effecting an inverse control such as to provide desired impulse responses between the output side of said adder means and said m input points; said inverse control system comprises n FIR filters disposed between said n receiving elements and the n input terminals of said adder means, respectively; a j-th(j=1, 2, . . . , n) one of said n FIR filters connected to a j-th one of said output points through an associated one of said receiving elements having a number Li of taps which satisfies the relationships represented by ##EQU27## for all i=1, 2, . . . , m and j=1, 2, . . . , n where wij is the number of discrete signals representing the impulse response gij (k) of said signal transmission channel between an i-th one of said m input points and the j-th output point of said linear FIR system and Pi is the number of discrete signals representing said desired impulse response ri (k) between said i-th input point and output side of said adder means; and said j-th FIR filter having filter coefficients hj (k) satisfying a relationship ##EQU28## for all i=1, 2, . . . , m where ○
* represents a discrete convolution. - View Dependent Claims (24, 25)
- n signal transmission channels between m input points and n output points, with n receiving elements being disposed at the respective n output points for receiving signals provided to said linear FIR system, wherein
Specification