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A linearly-constrained line-search adaptive filtering algorithm has been developed by incorporating the linear constraints into the least squares problem and searching the solution (filter weights) along the Kalman gain vector. The proposed algorithm performs close to the constrained recursive least squares algorithm while having a computational complexity comparable to the constrained least mean square algorithm. Simulations demonstrate its effectiveness. Refereed/Peer-reviewed

A streamlined theory is presented for adaptive filters within which the major adaptive filter algorithms can be seen as special cases. The algorithm development part of the theory involves three ingredients: a preconditioned Wiener Hopf equation, its simplest possible iterative solution through the Richardson iteration, and an estimation strategy for the autocorrelation matrix, the cross-correlation vector and a preconditioning matrix. This results in a generalised adaptive filter in which intuitively plausible parameter selections give the major adaptive filter algorithms as special cases. This provides a setting where the similarities and differences between the many different adaptive filter algorithms are clearly and explicitly exposed. Based on the authors' generalised adaptive filter, expressions for the learning curve, the excess mean square error and the mean square coefficient deviation are developed. These are general performance results that are directly applicable to the major families of adaptive filter algorithms through the selection of a few parameters. Finally, the authors demonstrate through simulations that these results are useful in predicting adaptive filter performance.

An adaptive IIR filter with a full-feedback structure is presented and a suitable LMS algorithm is derived. Using this algorithm, some examples are demonstrated where this structure has a distinct performance advantage over the conventional adaptive IIR filter structure.

The authors present an analytical model for the mean weight behaviour and weight covariance matrix of an adaptive interpolated FIR filter using the LMS algorithm to adapt the filter weights. The particular structure of this adaptive filter determines that special analytical considerations must be used. First, the introduction of an interpolating block cascaded with the adaptive sparse filter requires that the input signal correlations must be considered. It is well known that such correlations are disregarded by the independence theory, which is the basis for the analysis of the LMS algorithm adapting FIR structures. Secondly a constrained analysis is used to deal mathematically with the sparse nature of the adaptive section. Experimental results demonstrate the effectiveness of the proposed analytical models as compared with the results obtained by classical analysis.

A fast-convergence frequency-domain adaptive filter is described. A simple normalisation scheme in the frequency-domain optimum block algorithm (FOBA) is used to set the convergence factor separately in each frequency bin. This normalised FOBA (NFOBA) yields significant convergence improvements.

Two filter designs for adaptive least mean squares (LMS) filtering with sigma–delta modulated input signals are described. One implementation is multibit multiplier-free and operates entirely at the oversampling frequency of the sigma–delta signals; in the other design only the FIR filter operates at the oversampled frequency while the adaptive filtering algorithm is performed at the Nyquist rate. To circumvent any aliasing problems that may be caused by the downsampling process in the architecture and ensure convergence of the adaptive FIR filter it is necessary to attenuate the high-frequency sigma-delta quantisation noise that is present. To perform this task a multiplier-free, multistage IIR filter structure is used that requires considerably fewer computations than an equivalent FIR filter. The two adaptive LMS filter designs are analysed and their performance is compared with a conventional PCM system in terms of achievable minimum MSE and adaptation speed.

The concept of set membership (SM) adaptive filtering is extended to the frequency domain and a novel frequency domain SM algorithm is derived. Simulations show that the new SM algorithm has a much improved convergence rate over the conventional fast normalised least mean square (FNLMS) algorithm with identical misadjustment performance. Moreover, the SM algorithm has the same order of computational complexity as the FNLMS algorithm.

An adaptive filtering algorithm for artefact removal in block coded images is presented. Based on an analysis of block artefacts in the frequency domain, the edge image is notch filtered and then used for a neighbourhood analysis. A space-variant filter is applied to the coded image adaptively, dependent on a frequency analysis.

The multidelay block frequency domain (MDBFD) adaptive filter with the two-dimensional optimum block (TOB) algorithm are extended to the Hartley domain. The convergent behaviour of the MDBHD-TOB is the same as its frequency domain counterpart while computational complexity is reduced to offer simpler implementation. Because of its computational efficiency, the MDBHD-TOB adaptive filter is well suited to applications which demand the use of a long adaptive filter, as in acoustic echo cancellation.

A new linearly constrained adaptive filtering algorithm, the linearly constrained optimum block adaptive (LCOBA) algorithm, is presented. The LCOBA algorithm processes data in blocks and uses variable convergence factors which are optimised in a least square sense. It is superior to Frost's linearly constrained least mean squares algorithm at achieving the conflicting goals of fast convergence with little steady-state error. In addition, its computational requirements generally tend to be smaller than that of the Frost algorithm, as the block length is increased.

An adaptive approach to the design of linear phase low-pass FIR filters with extra constraints on filter coefficients is presented. In this approach, the procedures using the LMS adaptive algorithm are modified to include the constraints on the filter coefficients. Numerical examples are presented and compared to the results obtained using least-square design in the frequency domain in which the filter design problem is transformed into an equivalent nonlinear optimisation problem.

This letter describes the construction and operation of an adaptive filter based on the Widrow least-mean-square adaption algorithm using a 64-point analogue programmable c.c.d. transversal filter as the main processing element. Initial test results are presented to confirm the principle of the system and these results may be readily compared with previously published simulation results.