ECE352HW11set1 - The Ohio State University The Department...

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The Ohio State University The Department of Electrical and Computer Engineering ECE 352 Homework set 1, Winter 2011 Synopsis : This homework is essentially based on previous courses and previously learned material. Please refer to previous notes and text books for help. The emphasis is on continuous time linear time-invariant systems. Problem 1 (20) A periodic voltage signal x(t) is given in standard form ( sum of a sine and a cosine), by x(t)= 5 cos 4t + 12 sin 4t . The unit is a Volt). 1.1 Derive the average power of this signal in Watts ( delivered to a one Ohm resistor). 1.2 Express x(t) in laboratory form and derive its average power. 1.3 Express x(t)in exponential Fourier series form, give the magnitude and phase of its components and derive its average power. Problem 2 (20) Suppose the above signal is input, for all time, to an RC low pass filter with transfer function H(s)= 2/(s+2). The output is y(t). 2.1 Write an expression for the steady state response y(t).
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