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Unformatted text preview: EE 200 Fall 2009 (Weber) Homework 1
At the upper right corner on page 1 of all homeworks, show: Last name, First name Date EE 200, Homework # Show intermediate steps whenever possible. 1. Write the expression(s) that define the function plotted below. y 1 2 1 1 2 x 1
2. For the signal shown in the graph below, a. What is the period of the signal? x(t) 4 t (msec) 2 4
b. What is the frequency of the signal in Hz.? c. What is the amplitude of the signal (approximately) if the units on the vertical axis are Volts? d. What is , frequency of the signal in radians/second? 3. The "signum" function sgn(x) is defined as 1 x < 0 sgn(x) = 0 x=0 1 x>0 3 sgn(x) 2 f2 (x) = 2 sin(x) 3 4 6 8 Using the following functions f1 (x) = plot these composition functions over [2, 2] 1 a. (f1 f2 )(x) b. (f2 f1 )(x) 4. Do the following matrix operations. a. 4 6 3 1 = b. 5 6 4 3 = c. 1 4 2 3 2 6 5 2 7 3 = 5 8 d. 4 1 9 5 3 6 2 0 4 1 = 9 6 5. In the lab on Wednesday we will be measuring voltages using multimeters that measure the "RMS" (root mean square) voltage of a signal. The RMS voltage of a signal x(t)is defined as VRMS = where T is the period of the signal. a. Assume x(t) is given by x(t) = VP eak sin(2f0 t) where VP eak is the amplitude, f0 is the frequency of the sinusoid in Hz. and f0 = 1/T . Use the formula above for VRMS to derive the relationship between VP eak and VRMS . Hint: The trig identity cos 2 = 1  2 sin2 will come in useful. b. For household electric power VRMS is about 120 Volts. Based on your result above, what is the corresponding VP eak ? 1 T
T x2 (t)dt
0 2 ...
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This note was uploaded on 02/26/2010 for the course EE 30446 at USC.
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