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Exam 1 Spring 12 (1).jpg - ELEC-2120 Exam 1 spring 2012...

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Unformatted text preview: ELEC-2120 Exam 1 spring 2012 Problem 1.) and Problem 2.) are worth 15 points. Problem 3.) is worth 30 ' R‘ 5 points. Problem 4.) is worth 40 paints. ( Igg ) 1.) Accurately sketch the following functions: a.) x(t) = tum—(I — 2)u(t~— 2)—(t—4)u(t —4)+(t —6)u(t—6) b.) x[n] = (n+ 2)u[n + 2] _ 2u[n] enu[n — 4] 2.) Given y[n +1] + 0.8y[n] = x[n] compute y[n] for n=0, 1, and 2 when x[n] = u[n] and yl‘1]= 2- 3.) Consider the two continuous time functions given by: x(t) = 2[u(t) -u(t - 2)] and h(t) = 2[u(t — 3) — u(t — 5)] . a.) Accurately sketch the functions b.) Determine an analytical expression for the output of a linear system if x(t) is the system input and h(t) is the system impulse response function. c.) Accurately sketch the system output function. 4.) Consider the circuit shown below where the input function, x(t), is the voltage source and the output function is the current, yit) , that flows through the series combination of the resistor R and inductance L. Take R=1 o and L=1 H. a.) Write and expression for the input/output differential equation for this linear system. b.) Write and expression for the input/output discrete-ti me representation of the circuit. c.) Take T=.1 second, y[-1]=0, and x[n] = 6[n] and determine the unit pulse response for n=0,1, and Z. d.) Now take x(t)=u(t) and write out the MATLAB commands needed to solve the differential equation describing this linear system using ode45 for 0<t<8. ...
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