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Unformatted text preview: Lecture S19 Muddiest Points General Comments Today, we began our discussion of sampling theory. We found that if we sample a band-limited signal at more than twice its bandwidth, then we can reconstruct the signal exactly. Thats great, because it tells us how to design systems, such as CD players, that faithfully reproduce the original signal. Responses to Muddiest-Part-of-the-Lecture Cards (13 cards) 1. Im going to be honest what is a Fourier transform? How does it differ from Laplace, and when do we use Fourier? I should understand by now, but I dont get it. (1 students) At the most basic level, a FT is the same as a LT when the signal (say, g ( t )) is stable. When g ( t ) is unstable, there is no FT, although there may be a LT. However, for some signals (such as sinusoids), there is, strictly speaking, no FT or LT, because there is no region of convergence for which the LT converges. However, we can define a FT, if we do so carefully, in a limiting sense. This is good, because many signals of interest in communications (such as sinusoids) could not be analyzed by transform methods otherwise. 2. Basically with CDs, youre saying we sample at twice the rate of the signal, so we know the entire signal, because its linear? [There is a figure that basically...
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- Fall '05