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Laplace and Z Transforms - MIT

: Signals and SystemsLaplace and Z TransformsOctober 1, 2009 Mid-term Examination #1 Wednesday, October 7, 7:30-9:30pm, Walker recitations on the day of the :DT Signals and SystemsLectures 1 5 Homeworks 1 4 Homework 4 will include practice problems for mid-term , it will not collected or graded. Solutions will be book: 1 page of notes (812 11inches; front and back).Designed as 1-hour exam; two hours to sessions during open o ce ict? Contact before Friday, October 2, TimeMany continuous-time systems can be represented with di : leaky tankr0(t)r1(t)h1(t)Di erential equation representation: r1(t) =r0(t) r1(t)Last time we considered two methods to solve di erential equations: solving homogeneous and particular equatio

Laplace transform of a derivative Assume that X(s) is the Laplace transform of x(t): X(s) = Z ∞ −∞ x(t)e−stdt Find the Laplace transform of y(t) = ˙x(t). Y(s) = Z ∞ −∞ y(t)e−stdt = Z ∞ −∞ x˙(t)e−stdt = x(t)e−st ∞ ∞ −∞ − Z −∞ x(t)(−se−st)dt The rst term must be zero since X(s) converged. Thus Y(s ...

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