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Unformatted text preview: Lecture S12 Muddiest Points General Comments Today, we talked about the relationship between BIBO stability and the region of convergence. The neat result is that a system is BIBO stable if and only if the region of convergence of the Laplace transform of the impulse response contains the line Re[ s ] = 0. Responses to Muddiest-Part-of-the-Lecture Cards (17 cards) 1. What is the region of convergence? (1 student) Its the set of all values of s for which the Laplace transform integral converges. 2. Why does it matter that the LT integral converges absolutely as opposed to just converges? (1) Even though the LT might converge (but not absolutely) at the boundaries of the region of convergence, in the interior it will generally converge absolutely, because the integrand will be exponentially smaller (as t goes to either + or ) than at the boundary of the r.o.c. Thats good, because if the interior of the r.o.c. includes Re[ s ] = 0, then absolute convergence of the LT is the same as convergence of | g ( t ) dt | 3. Stop proving everything. We believe you. (1) But you need to understand why these things works. Its not satisfactory for me to just claim something is true you shouldnt believe it unless I prove it....
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.
- Fall '05