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When you have the cursor at the desired location, simply click. Your drawing displays the viewpoint that you specified. Along with the tripod and compass, you see the current UCS icon based on the current UCS to help you find your bearings. Figure 22.8 shows, on the left, the cursor location that results in the viewpoint shown on the right. This is very close to the SE isometric view. FIGURE 22.8

However, it could also be computed more directly (but also less efficiently) by using its definition, namely, p&(i) = u(i - M ) - u M , . j w L , i - l

Power normalization The use of NLMS, or of a power-nonnalized version of it as in Sec 281, in order to train the subband filters, can improve the rate of convergence of block filters as indicated by the analyses in Sommen et al (1987) and Lee and Un (1989) Constrained vs unconstrained implementationsIn Mansoni and Gray (1982), it was shown that the unconstrained DFT-based block adaptive filter can still work well if the filter length M is sufficiently large Still, unconstrained implementations are slow to converge (especially for M / B > 1) and they do not converge to the optimal solution On the other hand, it has been verified experimentally that the constraint does not need to be applied at every iteration Subband adaptive filters The concept of subband adaptive filtering was introduced by Furukawa (1984) and Kellermann (1984,1985).

(9.67)

Other early works in this area include Yasukawa and Shimada (1987,1993), Chen et al (1988), Gilloire and Vetterli (1988,1992), and Petraglia and Mitra (1993) Some further results on subband structures can be found, eg, in Morgan and Thi (1995), Pradhan and Reddy (1999), Farhang-Boroujeny (1999), Petraglia, Alves, and Diniz (2000), and the references therein The work by Morgan and Thi (1995) provides a useful approach to handling the delay problem that plagues subband architectures - see Prob VI14 The book by Farhang-Boroujney (1999) provides a good treatment of subband adaptive filters with emphasis on design issues Block and subband filters When the open- and closed-loop subband architectures of Sec 282 were proposed in the literature, the DFT-block adaptive filters of Sec 281 did not even exist So the derivations of these subband structures were not originally motivated in the same manner we discussed in Sec.

282, by showing how block and subband adaptive filters relate to each other In fact, one can verify that even the technical language used in the derivation of the DFT-block adaptive structure, eg, in So0 and Pang (1987,1990), has little resemblance with the language of modem multi-rate systems and filter banks (eg, as in Vaidyanathan (1993)) An application to acoustic echo cancellation As mentioned in the concluding remarks of Part IV (Mean-Square PerJomance), there are two types of echoes in communications systems: line echoes and acoustic echoes In Computer Project IV 1 we studied line echo cancellation and in Computer Project VI1 we shall study acoustic echo cancellation using block adaptive filters.

with 0 (0, 1] and mq (k) E{|y1 (k)| }, q = 2, 4. The above cost function is similar to = that already proposed by Shalvi and Weinstein [1067, 1069, 1204] and in an extended form by Inouye [612, 613] and Comon [307] for blind deconvolution problems [552]. However, 4 2 instead of the standard kurtosis (E{y1 } 3E 2 {y1 }), we employ a normalized one which eliminates any constraint on the variance of the output signals and therefore considerably simpli es the optimization procedure. Furthermore, the normalized kurtosis is more robust in respect to outliers and spiky noise. In some applications like communications, source signals are typically sub-Gaussian, so they have negative kurtosis. In such cases, the nonlinear function can be simpli ed as