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Unformatted text preview: Lecture S7 Muddiest Points General Comments Today, we talked about the role of transfer functions and the Laplace transform in Signals and Systems. We saw that the transfer function of any LTI system is the Laplace transform of the impulse response. Even better, the Laplace transform is a natural consequence of the LTI assumption. Responses to Muddiest-Part-of-the-Lecture Cards (36 cards) 1. Why is this the most important Signals lecture this term? (1 student) Because of the ideas in the General Comments above. This idea is the core of everything we do. 2. What is s in the Laplace Transform? (3) If you learn Laplace Transforms (LTs) as in 18.03, s appears out of the blue, so its just a transform variable, so the transforms turns function of t into functions of s . In our approach, the LT is connected to transfer functions, so the s corresponds the the exponent in e st . So s is a generalized frequency. In particular, if s = j , then the input is sinusoidal with frequency . 3. So Laplace is what comes out when the input is exponential, and Fourier comes out when the input is sinusoidal. (1) Yes, but of course these overlap when s = j , they are the same. 4. What are regions of convergence? (1) The Laplace transform integral converges only for some values of s . The set of values for which the transform converges is called the region of convergence. of convergence....
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- Fall '05