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1) (a)  Justify the small step-size theory of Section 6

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1) (a)  Justify the small step-size theory of Section 6.4, dealing with the infinite-precision LMS algorithm.  (b) How can stalling be prevented in the RLS algorithm? Suggest an appropriate method for stabilizing a digital implementation of the LMS algorithm whose leakage factor (1 − ma) in Eq. (12.19) has the equivalent effect of adding a white-noise sequence of zero mean and variance a to the input process u(n). Derive the formula to prevent the RLS algorithm from stalling due to digital effects by making the digital residual error eD(m) as small as possible.

2) Illustrate the assumptions in a statistical analysis of the finite-precision LMS algorithm.  Show that the total output mean-square error produced in the finite-precision algorithm has a steady-state composition. How can a leaky LMS algorithm be prevented from stalling due to digital effects? The error-propagation model of RLS algorithms considered in this chapter examines the “linearized” round-off propagation mechanism and focuses on the property of exponential stability. In reality, however, round-off error propagation in an RLS algorithm is a nonlinear mechanism. Explain.

3) Problem 17 of Chapter 6 addresses the application of the LMS algorithm to the design of a linear predictor operating on an autoregressive process of order two. Using the RLS algorithm, repeat parts (b) through (e) of the computer experiment described therein. Explain the close relationship of the LMS algorithm to stochastic approximation when there is a decrease in the value of the step-size parameter m with an increasing number of adaptation cycles.  Problem 20 of Chapter 6 addresses the application of the LMS algorithm to the study of an MVDR beamformer. Using the RLS algorithm, repeat the computer experiment described therein.

4) (a) Explain in detail the procedure to find the optimum value of the updated weight vector.  (b) Explain the procedure for solving a constrained optimization problem. Explain in detail how an affine projection adaptive filter converges at a rate faster than that of the corresponding normalized LMS algorithm.  Illustrate how an adaptive filter performs circular convolution instead of linear convolution.

5) What are the equations that define the operation of the LMS algorithm of the canonical model of the complex LMS algorithm? Set up the equations that define the operation of the LMS algorithm that is used to implement adaptive noise cancelling applied to a sinusoidal interference. Demonstrate that the LMS algorithm acts as a low-pass filter with a low cutoff frequency when the step-size parameter μ is small.

6) In a lattice-based structure for joint-process estimation, explain why the backward error prediction method is preferable to forward prediction. For m = 2, compute r(2) for the autocorrelation function and the reflection coefficients given P0, k1, k2, and k3. Find the inverse recursion using Levinson–Durbin recursion for the tap weights a3,1, a3,2, a3,3, and a4,4 of a prediction-error filter of order 3. Determine the corresponding reflection coefficient k1, k2, k3, and k4 for the order 4.

7) Determine the complex Gaussian process for the odd case of N = 5 with u(n) consisting of the five samples u1, u2, u3, u4, and u5. By using the Gaussian moment-factoring theorem, determine the complex Gaussian process for the even case of N = 2. U(n) consists of the samples u1 and u2. Prove that a random process {X (t)} is mean square continuous if its autocorrelation function is continuous.

8) A common advertising technique is to link a particular product with some other gratifications. For many years Marlboro cigarettes have been linked to the serenity and ruggedness of wide open pastures, for example, and a TV advertising campaign linked Old Milwaukee beer to parties with the “Swedish Bikini Team.” Legally speaking, why don’t such ads qualify as deceptive messages?

9) Do you think the definition for misleading advertising should encompass ads that are likely to mislead reasonable consumers, as the current FTC standard reads, or should plaintiffs and prosecutors have to prove that an ad actually did mislead reasonable consumers? Some members of the advertising industry have argued in favor of the latter standard. Or do you think the standard should move in the other direction, prohibiting advertising that could result in possible deception? This was the standard used in the 1970s

10) Based on the principles discussed in this chapter, is there any limit on the government’s ability to require warning messages in product advertising? For example, suppose Congress enacted a law stating that all advertising for high-calorie fast food must contain a boldface message citing various health statistics and warning consumers about dangers of eating fast food too frequently. Further suppose that the law requires the warning message to be enclosed in a box equal to one-third of the total space purchased for the ad. Should this be considered a substantial restriction on advertising, thereby invoking the Central Hudson test? At what point does a warning notice requirement work as a de facto ban on advertising?

11) In light of the decision in Bates v. State Bar of Arizona and the development of the Central Hudson test, do you think advertising bans on any of the professions could be constitutionally valid? Could physicians be prevented from truthfully advertising their services and fees in TV commercials or on billboards? Might any substantial justifications exist for such a ban?

12) Courts have drawn a distinction between over-the-air broadcasting and cable TV and have concluded that the FCC’s indecency prohibition cannot be applied to the latter. Cable is a less intrusive medium, the courts have said. Is this a valid distinction? Is electing to have a TV set in the home an affirmative action to the same extent as electing to subscribe to cable? And if a parent elects not to have cable TV in the home, is this a practical way of protecting children if indecent cable programming is nonetheless readily available in the community? Do your answers also apply to the Internet?

13) This chapter has examined two main approaches to controlling sexually explicit depictions. One is to describe a class of expression—obscenity— that is without First Amendment protection and thus open to criminal punishment. Another approach is to rely on zoning laws and other quasi–time/ place/manner restrictions to confine adult materials to places where they are unlikely to offend unwilling audiences or cause identified negative effects. Which of these approaches do you think is most effective? Which is most compatible with First Amendment ideals? Which best addresses legitimate moral concerns of society?

14) In his concurring opinion in the 1987 case of Pope v. Illinois, Supreme Court Justice Antonin Scalia said the justices’ variety of opinions evidenced a “need for reexamination of Miller.” If the Court were to undertake such a reexamination, what would be the most likely outcome? Some minor adjustments in the obscenity definition? Or do you think the current Court would be inclined to consider a whole new approach to obscenity and the First Amendment?

15) How would you devise a new, more workable legal standard for obscenity? Should the purpose of the communicator be considered? Should evidence of harmful effects be required, or should a presumption of moral harm be sufficient? Should the standard take into account whether the audience is willing or unwilling?

16) The Commission defines indecent speech as language that, in context, depicts or describes sexual or excretory activities or organs in terms patently offensive as measured by contemporary community standards for the broadcast medium. Indecency findings involve at least two fundamental determinations. First, the material alleged to be indecent must fall within the subject matter scope of our indecency definition—that is, the material must describe or depict sexual or excretory organs or activities. . . . Second, the broadcast must be patently offensive as measured by contemporary community standards for the broadcast medium

17) In this Notice of Apparent Liability for Forfeiture (“NAL”), we find that AMFM Radio Licenses, LLC (“AMFM”), licensee of Station WIHT(FM), Washington, D.C., apparently violated 18 U.S.C. § 1464 and 47 C.F.R. § 73.3999, by willfully broadcasting indecent language. Based upon our review of the facts and circumstances in this case, we conclude that AMFM is apparently liable for a monetary forfeiture in the amount of Twenty-Seven Thousand Five Hundred Dollars ($27,500.00), the applicable statutory maximum.

18) Do you see any evidence that the children’s TV programming requirement has had a positive impact in our society? As children shift more and more of their attention to the Internet and less time to TV, does it make sense to continue saddling TV broadcasters with the “kid-vid” programming rules?

19) On the other hand, is it a wise use of the nation’s airwaves to stick to a schedule of sophomoric TV sitcoms during the height of campaign season, making it difficult for new candidates and potential leaders to become known and to succeed? Would a significant amount of mandated, free air time for candidates actually improve national discourse, help us solve problems, and help us spot and elect tomorrow’s best leaders? Could such a system be devised with some safeguards against abuse, or would that violate the First Amendment?

20) Do you think the lowest-unit-rate limitation for candidate commercials is working in the public interest, or is it merely a statutory perk for candidates? Given the shallow, misleading, and even mean-spirited nature of today’s political advertising, should broadcasters be allowed to set extra high rates for political advertising if they wish?

21) Apart from the constitutional issues, media have criticized the Federal Communications Commission’s EEO requirements as overly burdensome paperwork and bureaucracy—especially for small broadcasters with only a handful of employees. But some consumer groups say that the electronic media, with their special power to influence, have an obligation to reflect the makeup of their communities. Do you think the FCC’s current EEO rules have struck a workable balance? What do broadcasters in your community think?

22) In striking down the FCC’s 30-percent national subscriber cap on cable companies, the federal appellate court in 2009 said the agency failed to show the rule was necessary to protect competitiveness in a marketplace of growing satellite video options. Discuss this further, from the financial perspective of a small production company. If the nation’s largest cable companyturns down a proposed TV show, does the production company still have viable options for reaching a large national audience? Or could that single cable company’s denial create a programming bottleneck?

23) The severe economic downturn of 2008 and 2009 led many media corporations to slash budgets, divest properties, and lay off employees, in some cases making the FCC’s ownership limits a moot point. But are there advantages to having at least a handful of very large media conglomerates in the nation? (Recall from earlier chapters that many of the most important First Amendment cases were initiated by large media companies with the substantial resources necessary to fight the government in court.)

24) The legal restraints on broadcast station ownership have proved highly controversial. Do you think the FCC makes a valid assumption that greater diversity of broadcast owners will equate to greater diversity in programming? Might another rationale better justify caps on ownership by a single individual or corporation?

25) Suppose the Supreme Court took the drastic step of overturning Red Lion and declaring invalid the current licensing scheme for broadcast. What kind of legal rules could be applied instead to ensure orderly use of frequencies and sufficient certainty to prompt capital investment in stations?

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