From a mixed signal in which a first signal and a second signal are mixed, the second signal is removed at low processing cost and without delay. As a result, an estimated first signal which has low residue of the second signal and low distortion is obtained. An estimated first signal is generated by subtracting a pseudo second signal which is estimated to be mixed in a first mixed signal in which a first signal and a second signal are mixed from the first mixed signal. The pseudo second signal is obtained by a first adaptive filter using a second mixed signal in which the first signal and the second signal are mixed in a different proportion from the first mixed signal. A coefficient update amount of the first adaptive filter is made smaller as compared with a case when the estimated first signal is smaller than the first mixed signal, in case the estimated first signal is larger than the first mixed signal.

A method is explained for any adaptive processor processing digital signals by adjusting signal weights on digital signal(s) it handles, to optimize adaptation criteria responsive to a functional purpose or externalities (transient, temporary, situational, and even permanent) of that processor. Adaptation criteria for the adaptive algorithm may be any combination of a signal or parameter estimation, and measured quality(ies).

This method performs a linear transformation adapting parameters from M to (M.sub.1+L) dimensions in each adaptation event, such that M.sub.1 weights are updated without constraints and M.sub.0=M−M.sub.1 weights are forced by soft constraints into an L-dimensional subspace they spanned at the beginning of the adaptation period. The same dimensionality reduction, using the same linear transformation, is applied to the input data. The reduced-dimensionality weights are then adapted using the identical optimization strategy employed by the processor, except with input data that has also been reduced in dimensionality.

An adaptive processor implements partial updates when it adjusts weights to optimize adaptation criteria in signal estimation, parameter estimation, or data dimensionality reduction algorithms. The adaptive processor designates some of the weights to be update weights and the other weights to be held weights. Unconstrained updates are performed on the update weights, whereas updates to the set of held weights are performed within a reduced-dimensionality subspace. Updates to the held weights and the update weights employ adapt-path operations for tuning the adaptive processor to process signal data during or after tuning.

An adaptive processor implements partial updates when it adjusts weights to optimize adaptation criteria in signal estimation, parameter estimation, or data dimensionality reduction algorithms. The adaptive processor designates some of the weights to be update weights and the other weights to be held weights. Unconstrained updates are performed on the update weights, whereas updates to the set of held weights are performed within a reduced-dimensionality subspace. Updates to the held weights and the update weights employ adapt-path operations for tuning the adaptive processor to process signal data during or after tuning.

An adaptive processor implements partial updates when it adjusts weights to optimize adaptation criteria in signal estimation, parameter estimation, or data dimensionality reduction algorithms. The adaptive processor designates some of the weights to be update weights and the other weights to be held weights. Unconstrained updates are performed on the update weights, whereas updates to the set of held weights are performed within a reduced-dimensionality subspace. Updates to the held weights and the update weights employ adapt-path operations for tuning the adaptive processor to process signal data during or after tuning.

A method is explained for any adaptive processor processing digital signals by adjusting signal weights on digital signal(s) it handles, to optimize adaptation criteria responsive to a functional purpose or externalities (transient, temporary, situational, and even permanent) of that processor. Adaptation criteria for the adaptive algorithm may be any combination of a signal or parameter estimation, and measured quality(ies). This method performs a linear transformation adapting parameters from M to (M.sub.1+L) dimensions in each adaptation event, such that M.sub.1 weights are updated without constraints and M.sub.0=M?M.sub.1 weights are forced by soft constraints into an L-dimensional subspace they spanned at the beginning of the adaptation period. The same dimensionality reduction, using the same linear transformation, is applied to the input data. The reduced-dimensionality weights are then adapted using the identical optimization strategy employed by the processor, except with input data that has also been reduced in dimensionality.

A method is explained for any adaptive processor processing digital signals by adjusting signal weights on digital signal(s) it handles, to optimize adaptation criteria responsive to a functional purpose or externalities (transient, temporary, situational, and even permanent) of that processor. Adaptation criteria for the adaptive algorithm may be any combination of a signal or parameter estimation, and measured quality(ies). This method performs a linear transformation adapting parameters from M to (M.sub.1+L) dimensions in each adaptation event, such that M.sub.1 weights are updated without constraints and M.sub.0=M?M.sub.1 weights are forced by soft constraints into an L-dimensional subspace they spanned at the beginning of the adaptation period. The same dimensionality reduction, using the same linear transformation, is applied to the input data. The reduced-dimensionality weights are then adapted using the identical optimization strategy employed by the processor, except with input data that has also been reduced in dimensionality.

An adaptive processor is configured to provide for reduced-complexity estimation of signal and data modes in high-dimensional data sets by implementing subspace-constrained partial updates to optimize an eigenvalue-based objective function. The adaptive processor selects, from a set of combiner weights, a set of update weights and a set of held weights; performs updates to the set of held weights within a reduced-dimensionality subspace and unconstrained updates to the set of update weights to produce updated combiner weights; and employs the updated combiner weights to determine at least one solution to an eigenequation or pseudo-eigenequation.

A method is described for reduced-complexity estimation of signal and data modes in high-dimensional data sets, by implementing subspace-constrained partial updates to optimize an eigenvalue-based objective function. The method selects, from a set of combiner weights, a set of update weights and a set of held weights; performs updates to the set of held weights within a reduced-dimensionality subspace and unconstrained updates to the set of update weights to produce updated combiner weights; and employs the updated combiner weights to determine at least one solution to an eigenequation or pseudo-eigenequation.