Advanced Concepts in Adaptive Signal Processing by W. Kenneth Jenkins, Andrew W. Hull, Jeffrey C. Strait,

By W. Kenneth Jenkins, Andrew W. Hull, Jeffrey C. Strait, Bernard A. Schnaufer, Xiaohui Li

Although adaptive filtering and adaptive array processing started with learn and improvement efforts within the overdue 1950's and early 1960's, it was once now not until eventually the e-book of the pioneering books by way of Honig and Messerschmitt in 1984 and Widrow and Stearns in 1985 that the sector of adaptive sign processing started to end up a special self-discipline in its personal correct. considering that 1984 many new books were released on adaptive sign processing, which serve to outline what we are going to check with all through this booklet as traditional adaptive sign processing. those books deal essentially with easy architectures and algorithms for adaptive filtering and adaptive array processing, with lots of them emphasizing functional purposes. lots of the current textbooks on adaptive sign processing concentrate on finite impulse reaction (FIR) clear out buildings which are proficient with options in keeping with steepest descent optimization, or extra accurately, the least suggest sq. (LMS) approximation to steepest descent. whereas actually 1000s of archival learn papers were released that take care of extra complicated adaptive filtering options, not one of the present books try to deal with those complicated techniques in a unified framework. The objective of this new publication is to give a couple of vital, yet now not so renowned, themes that presently exist scattered within the examine literature. The booklet additionally records a few new effects which have been conceived and built via study performed on the collage of Illinois prior to now 5 years.

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The upper signals labeled fj(n) are the corresponding forward prediction errors . , the lattice predictor, is properly converged, the set of backward prediction errors {bj(n)} forms an orthogonal basis for the input signal space. Therefore, one can interpret the lattice predictor as an "adaptive linear transformation" that decomposes the input signal x(n) into M+ 1 orthogonal components, which are then applied to the linear combiner to form a complete adaptive filter. When these signals are used with the power normalized LMS algorithm , the best possible convergence rate can be achieved.

1 A fast quasi-Newton algorithm The quasi-Newton algorithms discussed above achieve reduced computation through the use of particular autocorrelation estimators which lend themselves to efficient matrix inversion techniques. 23] . Considerable detail is given for this particular I-D algorithm in order to provide sufficient background for the 2-D extension of this algorithm that is treated in Chapter 3. To derive the O[N] fast quasi-Newton (FQN) algorithm, a different autocorrelation matrix estimate is used, which permits the use of more robust and efficient computation techniques .

The importance of this modification of the FQN algorithm is that a matrix inversion is now required only once every N time steps. Using the Levinson recursion, the average amount of computation required is now O[N2]/N, or O[N]. 33) should still be updated at each time step, so that an accurate autocorrelation estimate is maintained, although the 34 Advanced Concepts in Adaptive Filtering coefficient update process will use only every N-th estimate. The order of the computation achieved by this scheme could also be achieved using blocks whose lengths were multiples or submultiples of N.

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