By W. Kenneth Jenkins, Andrew W. Hull, Jeffrey C. Strait, Bernard A. Schnaufer, Xiaohui Li
Although adaptive filtering and adaptive array processing begun with examine and improvement efforts within the past due 1950's and early 1960's, it was once now not until eventually the book of the pioneering books via Honig and Messerschmitt in 1984 and Widrow and Stearns in 1985 that the sphere of adaptive sign processing started to end up a different self-discipline in its personal correct. due to the fact that 1984 many new books were released on adaptive sign processing, which serve to outline what we are going to discuss with all through this publication as traditional adaptive sign processing. those books deal essentially with simple architectures and algorithms for adaptive filtering and adaptive array processing, with a lot of them emphasizing useful purposes. lots of the present textbooks on adaptive sign processing specialise in finite impulse reaction (FIR) filter out constructions which are informed with options in keeping with steepest descent optimization, or extra accurately, the least suggest sq. (LMS) approximation to steepest descent. whereas actually thousands of archival study papers were released that care for extra complicated adaptive filtering recommendations, not one of the present books try and deal with those complicated techniques in a unified framework. The aim of this new booklet is to offer a few vital, yet no longer so renowned, issues that at present exist scattered within the examine literature. The booklet additionally files a few new effects which were conceived and constructed via learn carried out on the collage of Illinois in the past 5 years.
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Additional resources for Advanced Concepts in Adaptive Signal Processing
This leads to MSE surfaces that are typically not quadratic in nature. 7]. In these cases the LMS algorithm, being a gradient search technique, may converge to a local minimum, resulting in poor performance when used in practical applications . Therefore it can be concluded that as applied to IIR adaptive filters, the LMS algorithm is prone to difficulties. In general, practicing engineers are reluctance to use it in practical applications due to its uncertain performance . 19] . The optimization is then performed on a modified cost function that uses e(n) rather than e(n).
In spite of these serious problems, the class of IIR filters remains of great interest for its potential to solve problems which require the synthesis of very long impulse responses. 43]. 30] that is entirely devoted to the subject of IIR adaptive filtering in signal processing and control. The topic of IIR adaptive filters is revisited in several places throughout later chapters of this book. 4 develops the use of the Preconditioned Conjugate Gradient Method in an effort to improve the learning characteristics of adaptive IIR filters .
I). 2) where only one term (i=O) is used in the summation, resulting in hMS(n) = le(n)12. While the LMS seems to make a rather crude approximation at the very beginning, the approximation results in an unbiased estimator. In many applications the LMS algorithm is quite robust and is able to converge rapidly to a small neighborhood of the Wiener solution.. I4) where V E[ e 2 ] (n) is the gradient of the cost function with respect to the coefficient vector wen). IS) and yen) = x(n)Twi(n) . 14) . ) Since the LMS algorithm is so well documented in the literature and so frequently used in practice, we will not present any further derivation or analysis of it here .
Advanced Concepts in Adaptive Signal Processing by W. Kenneth Jenkins, Andrew W. Hull, Jeffrey C. Strait, Bernard A. Schnaufer, Xiaohui Li