By W. Kenneth Jenkins, Andrew W. Hull, Jeffrey C. Strait, Bernard A. Schnaufer, Xiaohui Li
Although adaptive filtering and adaptive array processing begun with study and improvement efforts within the overdue 1950's and early 1960's, it used to be no longer until eventually the ebook of the pioneering books through 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 special self-discipline in its personal correct. given that 1984 many new books were released on adaptive sign processing, which serve to outline what we'll confer with all through this ebook as traditional adaptive sign processing. those books deal basically with easy architectures and algorithms for adaptive filtering and adaptive array processing, with lots of them emphasizing functional functions. lots of the present textbooks on adaptive sign processing specialise in finite impulse reaction (FIR) filter out buildings which are educated with ideas in keeping with steepest descent optimization, or extra accurately, the least suggest sq. (LMS) approximation to steepest descent. whereas actually enormous quantities of archival examine papers were released that take care of extra complicated adaptive filtering techniques, not one of the present books try and deal with those complicated recommendations in a unified framework. The aim of this new publication is to provide a few very important, yet now not so popular, subject matters that at the moment exist scattered within the learn literature. The booklet additionally files a few new effects which were conceived and built via learn performed on the college of Illinois in the past 5 years.
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Extra resources for Advanced Concepts in Adaptive Signal Processing
The FQN algorithm is extended to the case of 2-D FIR adaptive filters in Chapter 3. While the simple Toeplitz property for the autocorrelation matrix is lost in the 2-D case, the 2-D autocorrelation is found to have a Toeplitz block-Toeplitz structure that can be exploited to achieve a 2-D FQN algorithm that is similar to the FQN for the I-D case . 13]. In fact, there is so much literature on the analysis and performance of adaptive lattice filters that we will make no attempt to give this subject a comprehensive treatment here .
From this line of reasoning it becomes clear that white noise is the ideal input signal for rapidly training an LMS adaptive filter. The adaptive process becomes slower and requires more computation for input signals that are more severely colored. Convergence properties are reflected in the geometry of the MSE surface, which is simply the mean squared output error E[e(n)2] expressed as a function of the N adaptive filter coefficients in (N+ Ij-space. 44]). 7. 9]. 7 shows three equal-error contours on the three dimensional surface.
7. 9]. 7 shows three equal-error contours on the three dimensional surface. 14) is a quadratic form that describes the bowl shape of the FIR error surface. When R x is positive definite , the equal-error contours of the surface are hyperellipses (N dimensional ellipses) centered at the origin of the coefficient parameter space. 3]. Since the convergence rate of the LMS algorithm is inversely related to the ratio of the maximum to the minimum eigenvalues of R x, large eccentricity of the equal-error contours implies slow convergence of the adaptive system .