Filter arrangement implementing a least squares method utilizing rotation matrices

Claim 2

Filter arrangement implementing a least squares method comprising input means for receiving samples x(n+1) , evaluation means for evaluating angle functions θ i =(i=1 to N), which angle functions form part of at least one of a plurality of rotation matrices, evaluation means for evaluating a gain vector G N (n+1) based on the rotation matrices, processor means for processing reference samples Y(n+1), evaluation means for evaluating an error signal e(n+1) in cooperation with the processor means, means for evaluating filtered samples y(n+1) recurring as a function of the angles θ i , of the gain vector, and of the error signal, whereby the filtered samples are accessible, wherein n, i, and N are integers.

Claim 3

Filter arrangement as claimed in claim 1, characterized in that it comprises a Table for producing the sine/cosine value of an angle as a function of its cosine/sine value.

Claim 4

Digital transmission system comprising a transmitter connected to a receiver by a transmission channel, this receiver comprising a filter arrangement implementing a least squares method comprising input means for receiving samples x(n+1), evaluation means for evaluating angle functions θ i =(i=1 to N), which angle functions form part of at least one of plurality of rotation matrices, evaluation means for evaluating a gain vector G N (n+1) based on the rotation matrices, processor means for processing reference samples y(n+1), evaluation means for evaluating an error signal e(n+1) in cooperation with the processor means, means for evaluating filtered samples y(n+1) recurring as a function of the angles θ i , of the gain vector, and of the error signal, whereby the filtered samples are accessible, and a decision element for deriving the reference samples from the filtered samples, where n, i, and N are integers.

Claim 5

Digital transmission system comprising a transmitter connected to a receiver by a transmission channel, this receiver comprising a filter arrangement implementing a least squares method comprising input means for receiving samples x(n+1), evaluation means for evaluating angle functions θ i =(i=1 to N), which angle functions form part of at least one of plurality of rotation matrices, evaluation means for evaluating a gain vector G N (n+1) based on the rotation matrices, processor means for processing reference samples y(n+1), evaluation means for evaluating an error signal e(n+1) in cooperation with the processor means, means for evaluating filtered samples y(n+1) recurring as a function of the angles θ i , of the gain vector, and of the error signal, whereby the filtered samples are accessible, and a decision element for deriving the reference samples from the filtered samples, where n, i, and N are integers.

Claim 6

A digital filter for implementing a least squares calculating comprising input means for receiving signals x(n+1); input means for receiving reference signals y(n+1); output means for supplying error signals e(n+1); processing means for calculating a plurality of matrices at least one of which includes angle functions θ i (i=1 to N); a gain vector G N (n+1) based on the rotation matrices; the error signals e(n+1), based on the reference signals; filtered signals y(n+1) as a function of the angles θ i , the gain vector G N (n+1), and of the error signals e(n+1); output means for supplying the filtered signals y(n+1).

Claim 7

A digital filter for implementing a least squares calculating comprising input means for receiving signals x(n+1); input means for receiving reference signals y(n+1); output means for supplying error signals e(n+1); processing means for calculating a plurality of matrices at least one of which includes angle functions θ i (i=1 to N); a gain vector G N (n+1) based on the rotation matrices; the error signals e(n+1), based on the reference signals; filtered signals y(n+1) as a function of the angles θ i , the gain vector G N (n+1), and of the error signals e(n+1); output means for supplying the filtered signals y(n+1).

Claim 8

Filter arrangement as claimed in claim 4, wherein the processing means evaluates the following: ##EQU20## where W is an omission factor such that 0<<W<1 Y' q;1 (n+1), Y' q;i (n+1), and Y' q;N (n+1 are all components of a vector Y' q (n+1) Y q;1 (n+1), Y q;i (n+1), Y q;n (m+1) are all components of a vector Y q (n+1).

Claim 9

Filter arrangement as claimed in claim 5, characterized in that the samples x(n+1) are normalized relative to their power, according to the following equation: ##EQU21## where represents the energy of the error signal ψ is the angle whose tangent is the square root of E.

Claim 10

Filter arrangement as claimed in claim 6, characterized in that for effecting this normalization it comprises a Table for producing a sin/cos value of an angle as function of its tg/cotg value.

Claim 11

A digital transmission system comprising a transmitter and a receiver which includes the filter of claim 4.

Claim 12

The filter of claim 4 wherein the processing means comprises look-up table means for supplying trigonometric function values.

Claim 13

The filter of claim 4 further comprising means, coupled between the output means for supplying the filtered signals and the input means for receiving the reference signals, for deriving the reference signals from the filtered signals.