By W. Kenneth Jenkins, Andrew W. Hull, Jeffrey C. Strait, Bernard A. Schnaufer, Xiaohui Li
Although adaptive filtering and adaptive array processing all started with study and improvement efforts within the past due 1950's and early 1960's, it used to be no longer till 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 become a different self-discipline in its personal correct. considering the fact that 1984 many new books were released on adaptive sign processing, which serve to outline what we'll check with all through this ebook 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 functions. many of the current textbooks on adaptive sign processing concentrate on finite impulse reaction (FIR) filter out constructions which are expert with innovations according to steepest descent optimization, or extra accurately, the least suggest sq. (LMS) approximation to steepest descent. whereas actually 1000s of archival examine papers were released that care for extra complex adaptive filtering thoughts, not one of the present books try and deal with those complicated thoughts in a unified framework. The aim of this new publication is to offer a couple of vital, yet now not so popular, issues that at the moment exist scattered within the study literature. The booklet additionally records a few new effects which have been conceived and built via examine performed on the collage of Illinois in past times 5 years.
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Extra resources for Advanced Concepts in Adaptive Signal Processing
The filter itself requires N multipl ications and N-I additions to produce yen) at each value of n. The coefficient update algorithm requires 2N multiplications and N additions, resulting in a total computational burden of 3N multiplications and 2N-I additions per iteration. Since N is generally much larger than the factor of three, the order of complexity of this algorithm is clearly O[N]. Furthermore since the order of complexity of the filter is the same as that of the coeffi cient update computation, the design goal stated earlier of achieving a complexity for the learning algorithm that is no greater than that of the filter itself has been achieved with the LMS algorithm .
E. e(n) =den) - yen). Strategies for obtaining an 20 Advanced Concepts in Adaptive Filtering appropriate den) vary from one application to another. In many cases the availability of a suitable training signal determines whether an adaptive filtering solution will be successful in a particular application. 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 addition to the discrete Fourier transform (DFT), other orthogonal transforms such as the discrete cosine transform (DCT) and the Walsh Hadamard transform (WHT) can also be Introduction and Background 23 10 I I " '" , t: ~ . '" I \ I .... "" \ '\ \ R x =[ ' .. " , \, .... I \ .... \.... ' .... \ .... \ .... \ .... 0 , ' \ .... 7 A 2-D error surface with a colored input signal. effectively used as a means to improve the LMS algorithm without adding too much additional computational complexity .
Advanced Concepts in Adaptive Signal Processing by W. Kenneth Jenkins, Andrew W. Hull, Jeffrey C. Strait, Bernard A. Schnaufer, Xiaohui Li