Signal processing system involving a least squares method

Signal processing system for implementing a least squares calculation, this system comprising:

• an input for receiving a sample x(n+1) at an instant n+1,
• another input for receiving at the instant a reference sample y(n+1),
• calculation means for minimizing a signal e(n+1) that represents a difference between the received sample and the reference sample, the calculation means operating according to a least squares calculation that utilizes rotation matrices Q.sub.a and Q.sub..alpha., the matrices being related to trigonometric functions, the calculation means comprising normalizing means for normalizing the received samples relative to a function of their energy, and
• memory means for storing a table of the trigonometric functions and for interacting with the calculating means which is for evaluating the trigonometric functions, and
• wherein the calculation means comprises prediction means:
• a) for evaluating the following quantities ##EQU56## where e'.sub.aq is a transformed prediction error and X'.sub.q is a transformed input sample vector,
• b) for updating the rotation matrix Q.sub..alpha.,
• c) for evaluating the quantity E.sub.a (n+1) on the basis of the following equation:
• ##EQU57## where Q.sub..alpha..sup.-1 is the inverse matrix of the matrix Q.sub..alpha.,
• d) for evaluating the quantity .alpha..sub.2 which is a normalized prediction error:
• .alpha..sub. =.gamma..sub. N.e'.sub.aq (n+1)E.sub.a.sup.1/2 (n+1)
• where .gamma..sub.N is the filter-error to prediction-error ratio,
• e) for evaluating the quantities:
• ##EQU58## where g.sub.N+1 is a component of an additional vector and G.sub.N is the transformed unit vector,
• f) for updating the matrix Q.sub.a, and
• g) for evaluating the quantities:
• ##EQU59##

Signal processing system for implementing a least squares calculation, this system comprising:

• an input for receiving a sample x(n+1) at an instant n+1,
• another input for receiving at the instant a reference sample y(n+1),
• calculation means for minimizing a signal e(n+1) that represents a difference between the received sample and the reference sample, the calculation means operating according to a least squares calculation that utilizes rotation matrices Q.sub.a and Q.sub..alpha., the matrices being related to trigonometric functions, the calculation means comprising normalizing means for normalizing the received samples relative to a function of their energy, and
• memory means for storing a table of the trigonometric functions and for interacting with the calculating means which is for evaluating the trigonometric functions,
• wherein the calculation means comprises initialization means for setting:
• =the cosine values at "1"
• =the sine values at "0"
• =values of the components of the vector X'.sub.q being a transformed input sample vector at "0"
• =values of the components of the vector Y.sub.q being a transformed reference sample vector at "0", and
• wherein prediction means are additionally provided for supplying the prediction error signal e(n+1) by evaluating the quantity:
• e(n+1)=.gamma.(n)e'.sub.aq (n+1).

Signal processing system for implementing a least squares calculation, this system comprising:

• an input for receiving a sample x(n+1) at an instant n+1,
• another input for receiving at the instant a reference sample y(n+1),
• calculation means for minimizing a signal e(n+1) that represents a difference between the received sample and the reference sample, the calculation means operating according to a least squares calculation that utilizes rotation matrices Q.sub.a and Q.sub..alpha., the matrices being related to trigonometric functions, the calculation means comprising normalizing means for normalizing the received samples relative to a function of their energy, and
• memory means for storing a table of the trigonometric functions and for interacting with the calculating means which is for evaluating the trigonometric functions, and
• wherein the calculation means comprise updating means for updating the rotation matrix Q.sub..alpha. causing angles .alpha..sub.i to occur by evaluating:
• ##EQU61## where X.sub.aq;i are the various components of the vector X.sub.q.

Signal processing system for implementing a least squares calculating, this system comprising:

• an input for receiving a sample x(n+1) at an instant n+1,
• another input for receiving at the instant a reference sample y(n+1),
• calculation means for minimizing a signal e(n+1) that represents a difference between the received sample and the reference sample, the calculation means operating according to a least squares calculation that utilizes rotation matrices Q.sub.a and Q.sub..alpha., the matrices being related to trigonometric functions, the calculation means comprising normalizing means for normalizing the received samples relative to a function of their energy, and
• memory means for storing a table of the trigonometric functions and for interacting with the calculating means which is for evaluating the trigonometric functions, and
• wherein the calculation means comprise updating means for updating the rotation matrix Q.sub.a causing angles .theta..sub.1 to occur by evaluating:
• ##EQU62## where g.sub.N-i is the N.sup.ith component of the transformed unit vector.

Signal processing system for implementing a least squares calculation, this system comprising:

• an input for receiving a sample x(n+1) at an instant n+1,
• another input for receiving at the instant a reference sample y(n+1),
• calculation means for minimizing a signal e(n+1) that represents a difference between the received sample and the reference sample, the calculation means operating according to a least squares calculation that utilizes rotation matrices Q.sub.a and Q.sub..alpha., the matrices being related to trigonometric functions, the calculation means comprising normalizing means for normalizing the received samples relative to a function of their energy, and
• memory means for storing a table of the trigonometric functions and for interacting with the calculating means which is for evaluating the trigonometric functions, and
• wherein there is provided the Table whose input is a tangent and whose output a sine, a second Table whose input is a sine and whose output is a cosine.

Signal processing system for implementing a least squares calculation, this system comprising

• an input for receiving a sample x(n+1) at an instant n+1,
• another input for receiving at the instant a reference sample y(n+1),
• calculation means for minimizing a signal e(n+1) that represents a difference between the received sample and the reference sample, the calculation means operating according to a least squares calculation that utilizes rotation matrices Q.sub.a and Q.sub..alpha., the matrices being related to trigonometric functions, the calculation means comprising normalizing means for normalizing the received samples relative to a function of their energy, and
• memory means for storing a table of the trigonometric functions and for interacting with the calculating means which is for evaluating the trigonometric functions, and
• wherein there is provided the Table for updating the matrix Q.sub.a, the input of this Table being a sine and its output a cosine, whereas the updating means of the matrix Q.sub.a evaluate:
• ##EQU63## and .gamma..sub.N =1/.gamma.'.sub.N.

Signal processing system for implementing a least squares calculation, this system comprising:

• an input for receiving a sample x(n+1) at an instant n+1,
• another input for receiving at the instant a reference sample y(n+1),
• calculation means for minimizing a signal e(n+1) that represents a difference between the received sample and the reference sample, the calculation means operating according to a least squares calculation that utilizes rotation matrices Q.sub.a and Q.sub..alpha., the matrices being related to trigonometric functions, the calculation means comprising normalizing means for normalizing the received sample relative to a function of energy, and
• memory means for storing a table of the trigonometric functions and for interacting with the calculating means which is for evaluating the trigonometric functions.

Signal processing system for performing echo cancelling using a least squares calculation, said system comprising:

• an input for receiving a sample x(n+1) at an instant n+1,
• another input for receiving at the instant a reference sample y(n+1),
• calculation means for performing echo cancelling by minimizing a signal e(n+1) that represents a difference between the received sample and the reference sample, the calculation means operating according to a least squares calculation that utilizes rotation matrices Q.sub.a and Q.sub..alpha., the matrices being related to trigonometric functions, the calculation means comprising normalizing means for normalizing the received samples relative to a function of their energy, and
• memory means for storing a table of the trigonometric functions and for interacting with the calculating means which is for evaluating the trigonometric functions, and
• wherein the normalizing means normalizes the received samples by a normalization factor E.sub.0.sup.1/2 (n+1), by determining an angle .psi. and the factor E.sub.0.sup.1/2 (n+1), as a function of a previous factor E.sub.0.sup.1/2 (n) and the received sample, by resolving:
• ##EQU64## where W.sup.1/2 is an omission factor.

Signal processing system for eliminating radio communication multipaths using a least squares calculation, said system comprising:

• an input for receiving a sample x(n+1) at an instant n+1,
• another input for receiving at the instant a reference sample y(n+1),
• calculation means for eliminating radio communication multipaths by minimizing a signal e(n+1) that represents a difference between the received sample and the reference sample, the calculation means operating according to a least squares calculation that utilizes rotation matrices Q.sub.a and Q.sub..alpha., the matrices being related to trigonometric functions, the calculation means comprising normalizing means for normalizing the received samples relative to a function of their energy, and
• memory means for storing a table of the trigonometric functions and for interacting with the calculating means which is for evaluating the trigonometric functions
• wherein the normalizing means normalizes the received samples by a normalization factor E.sub.0.sup.1/2 (n+1), by determining an angle .psi. and the factor E.sub.0.sup.1/2 (n+1), as a function of a previous factor E.sub.0.sup.1/2 (n) and the received sample, by resolving:
• ##EQU65## where W.sup.1/2 is an omission factor.

Signal processing system for performing signal prediction using a least squares calculation, said system comprising:

• an input for receiving a sample x(n+1) at an instant n+1,
• another input for receiving at the instant a reference sample y(n+1),
• calculation means for performing signal prediction by minimizing a signal e(n+1) that represents a difference between the received sample and the reference sample, the calculation means operating according to a least squares calculation that utilizes rotation matrices Q.sub.a and Q.sub..alpha., the matrices being related to trigonometric functions, the calculation means comprising normalizing means for normalizing the received samples relative to a function of their energy, and
• memory means for storing a table of the trigonometric functions and for interacting with the calculating means which is for evaluating the trigonometric functions
• wherein the normalizing means normalizes the received samples by a normalization factor E.sub.0.sup.1/2 (n+1), by determining an angle .psi. and the factor E.sub.0.sup.1/2 (n+1) as a function of a previous factor E.sub.0.sup.1/2 (n) and the received sample, by resolving:
• ##EQU66## where W.sup.1/2 is an omission factor.

Signal processing system for performing adaptive filtering using a least squares calculation, said system comprising:

• an input for receiving a sample x(n+1) at an instant n+1,
• another input for receiving at the instant a reference sample y(n+1),
• calculation means for performing adaptive filtering by minimizing a signal e(n+1) that represents a difference between the received sample and the reference sample, the calculation means operating according to a least squares calculation that utilizes rotation matrices Q.sub.a and Q.sub..alpha., the matrices being related to trigonometric functions, the calculation means comprising normalizing means for normalizing the received samples relative to a function of their energy, and
• memory means for storing a table of the trigonometric functions and for interacting with the calculating means which is for evaluating the trigonometric functions
• wherein the normalizing means normalizes the received samples by a normalization factor E.sub.0.sup.1/2 (n+1) by determining an angle .psi. and the factor E.sub.0.sup.1/2 (n+1), as a function of a previous factor E.sub.0.sup.1/2 (n) and the received sample by resolving:
• ##EQU67## where W.sup.1/2 is an omission factor.