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 no longer until eventually the ebook of the pioneering books via Honig and Messerschmitt in 1984 and Widrow and Stearns in 1985 that the sector of adaptive sign processing started to turn out to be a unique self-discipline in its personal correct. considering 1984 many new books were released on adaptive sign processing, which serve to outline what we are going to seek advice from all through this booklet as traditional adaptive sign processing. those books deal essentially with uncomplicated architectures and algorithms for adaptive filtering and adaptive array processing, with a lot of them emphasizing functional functions. many of the present textbooks on adaptive sign processing concentrate on finite impulse reaction (FIR) clear out constructions which are informed with ideas in accordance with steepest descent optimization, or extra accurately, the least suggest sq. (LMS) approximation to steepest descent. whereas actually hundreds of thousands of archival examine papers were released that take care of extra complicated adaptive filtering techniques, not one of the present books try to deal with those complicated ideas in a unified framework. The objective of this new e-book is to provide a few vital, yet no longer so renowned, themes that presently exist scattered within the examine literature. The e-book additionally files a few new effects which were conceived and built via learn carried out on the college of Illinois up to now 5 years.
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Additional info for Advanced Concepts in Adaptive Signal Processing
Thus the normalization can be safely ignored. 2 Efficient implementation of the FQN algorithm Although the FQN algorithm may appear to be an arbitrary member of the quasi-Newton class, it is distinguished by the fact that it can be implemented very efficiently. The greatest computational burden involved in the implementation of a general case quasi-Newton algorithm is in the inversion of the autocorrelation matrix estimate for use in the coefficient update. The unique feature of the FQN algorithm is that its autocorrelation matrix estimate is Toeplitz and symmetric .
The ideal cost function is defined by the mean squared error (MSE) criterion, equation (1. 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).
The current filter parameters now depend upon previous filter coefficients, which are time-varying. 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 .
Advanced Concepts in Adaptive Signal Processing by W. Kenneth Jenkins, Andrew W. Hull, Jeffrey C. Strait, Bernard A. Schnaufer, Xiaohui Li