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By Haykin S., Totterdill P.

At a degree appropriate for graduate classes on adaptive sign processing, this textbook develops the mathematical idea of varied realizations of linear adaptive filters with finite-duration impulse reaction, and in addition offers an introductory therapy of supervised neural networks. a variety of desktop experiments illustrate the underlying concept and functions of the LMS (least mean-square) and RLS (recursive-least-squares) algorithms, and difficulties finish each one bankruptcy.

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C o r ( » = Kk(jco)Knk(ja>) where Knk{jm) (34) is the complex amplification factor of the un­ connected system. Considering the L A F C , we obtain: Lcor(co) = L*(o>) + Lnk(a>) (34a) 34 AUTOMATIC CONTROL CIRCUITS that is, the L A F C of the corrected system is obtained by adding together the LAFCs of the uncorrected system and of the correct­ ing element. Figure 19b shows the correction of an automatic regulation system with the aid of the error of the differential. A comparison dBlLM dB L(cu) φ(ω) φ(ω) log ω / dec fa) FIG.

19a, 20a, and 2 1 , correspond to idealized elements. Actual correcting devices, 36 AUTOMATIC CONTROL CIRCUITS which are examined in the second part of this book, have LAFCs and LPFCs which coincide with the characteristics of the idealized elements, in given frequency bands. i I φ(ω) 1_(ω) 2 *? <7 y /U-<£> S< ^ + Χ(ω) k / " I, φ(ω) FIG. 21. 2 - Ιοςω dec IT 2 LAFC and LPFC of a series correcting device for which Methods of Parallel Correction T h e parallel correction of automatic regulation systems is effected, as has already been said, by the introduction of a local negative feed-back loop, which includes some part of the un­ connected system.

C is included in the feed-back loop. T h e correcting action of such a feed-back loop is shown in Fig. 23. 0 and once for ω" [ω' < ω"]. For frequencies when ω < ω' and ω > ω" the L A F C of the corrected and uncorrected systems coincide. 0 This characteristic represents a broken straight line with slopes of — 20 dB/d and — 40 dB/d. T h e frequency, corresponding to the break, is ω = l/T3. Figure 23 shows that the stability and required phase reserve of the system are obtained by attenuating the middle frequencies.

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Adaptive Filter Theory by Haykin S., Totterdill P.


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