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Affine projectionalgorithms Although LMS and NLMS are among the most widely used adaptive filters due to their computational simplicity and ease of implementation, colored input signals can deteriorate their convergence speed - see, eg, App 9D of Sayed (2003) To address this problem, Ozeki and Umeda (1984) developed the basic form of the affine projection algorithm (APA) Since then, many variants of APA (also known as data-reusing algorithms) have been devised from different perspectives such as the partial-rank algorithm (PRA) by Kratzer and Morgan (1983, the generalized NLMS algorithm by Morgan and Kratzer (1996), the decorrelating algorithm by Rupp (1998a), the APA with orthogonal correction factors (referred to as NLMS-OCF by Sankaran and Beex (1997,2000)), and the binomalized data-reusing LMS algorithm (which corresponds to the special case K = 2 of APA - see Apolinirio, Campos, and Diniz (2000)).

(5.28)

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An early analysis of data-reusing algorithms appears in Roy and Shynk (1989) A more recent study of an APA family appears in Shin and Sayed (2004) For applications of APA to acoustic echo cancellation, see the book by Benetsy et al (2001) Variable step-size LMS As we are going to see in s 16 and 24, the step-size in LMS adaptation controls the rate of convergence and the steady-state performance of the filter In order to meet the conflicting requirements of fast convergence and good steady-state performance, the step-size needs to be controlled Various schemes for controlling the step-size of LMS have been proposed in the literature, for instance, by Kwong and Johnston (1992), Mathews and Xie (1993), Aboulnasr and Mayyas (1997), Pazaitis and Constantinides (1999), and Shin, Sayed, and Song (2004a).

P With the restriction that n[Z jcn j2 is nite, f0 (x) [ L 2(R) and the family of functions {fn (x) b0 (x n)} forms an orthonormal basis of a subspace V0 , L2 (R). Evaluating the inner product b0 (x m)j f0 using the orthogonality relationship 0 b (x m)jb0 (x n) dnm we see from Eqn. (3.102) that

Kwong and Johnston (1992) use squared instantaneous errors, while Aboulnasr and Mayyas (1997) use the squared autocorrelation of errors at adjacent times, Pazaitis and Constantinides (1999) adopt the fourth-order cumulant of the instantaneous error, and Shin, Sayed, and Song (2004a) attempt to maximize the decrease in the weight-error-vector energy The step-sizes in these variants are evaluated in the manner shown in Table 143 (for the case of real data) Blind algorithms Blind algorithms compensate for the lack of an explicit reference signal They are pointedly referred to as adaptive algorithms for restoring signal properties by Treichler, Johnson, and Larimore (2001) One of the first blind algorithms in the context of signal processing is that of Griffiths (1967), who replaced the product u;d(i)in the LMS update (1010) by R d u , in which case.

(A.23)

Summary

People may sometimes not be susceptible to change, at least not quickly. So organisations should prepare for change by adopting a management programme that will be effective. The discussion of this chapter provides a platform for implementing a successful change programme.

Graph ofthe function (A.42).

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You can copy and paste pages within a PDF document or from one open PDF document to another. To copy a page with thumbnails, hold down the Ctrl/Option key as you drag a page to a new location in the same PDF file. Release the mouse button when you see the vertical highlight bar appear at the desired location. To copy a page from one PDF to another, open both PDF files and view them tiled either vertically or horizontally. The Pages panel must be in view on both PDF documents. Click and drag the thumbnail from one file to the Pages panel in the other document. The vertical highlight bar appears and the cursor changes, as shown in Figure 16.9. After the vertical bar is positioned at the desired location, release the mouse button, and the page drops into position.

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