Continuous-Time System Analysis usingSystem Analysis using the Laplace TransformWhy bother?•Analysis of continuous-time systems•Easier way to solve differential (system) equationsLaplace Transform4-1•Time-domain vs. frequency-domain
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Objectives•Be able to calculate the Laplace transform of a function directly from the integral, sketch the region of convergenceBe able to calc late the Laplace transform and its in ersesing the•Be able to calculate the Laplace transform and its inverse using the table of transforms and the properties of the Laplace transform•Be able to use partial fraction expansion to help calculate the inverseBe able to use partial fraction expansion to help calculate the inverse Laplace transform of a ratio of two polynomials•Be able to compute the impulse response of a linear constant coefficient differential equation using the Laplace transform•Be able to use the Laplace transform to simplify convolutions•Be able to determine the frequency response of a system from the Laplace transform and sketch it (Bode plots)Laplace Transform•Be able to explain tradeoffs between choosing a particular filter as a function of the number of poles. 4-2