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EE 207_101 Fall 2010 Graded HW 4 Due Date: Jan. 15, 2011 (groups of 2 students) Problem 1: A. For the circuit below, the switch is in open position before t = 0, then closed instantaneously at t =0. 1. Determine the initial capacitor voltage vC(0-) and the initial inductor current iL(0-). 2. Determine the output voltage across the capacitor, vC(t), using s-domain analysis. closes at t = 0 S1 R1 5 ohm R2 1 ohm R3 4 ohm + - Vs1 40V L1 2 H C1 1 F B. Determine the inverse Laplace transform of each of the following function: 3e2 s Y ( s) ( s 1)( s 2) Problem 2: A signal is given by x(t ) 5 6 cos 40 t . 1) x(t ) is sampled at sampling frequency f s 1 55Hz . Determine the spectrum of the sampled signal, X s1 ( f ) , and plot it ( up to + 80 Hz). Can we reconstruct x(t) from its sample values x(n)? if yes, explain how? 2) Repeat (1) with f s 2 35Hz . ( plot the spectrum up to 60Hz ) Problem 3: The Z-Transofrm of a signal x(n) is given by: with ROC: 0.5 | z | 3 , Find x(n) X (z ) 5 8z 1 (1 0.5z 1 )(1 3z 1 )