HW2.spring.2008.SOLUTIONS

# HW2.spring.2008.SOLUTIONS - ECE 2704 Homework Number 1 Due...

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Unformatted text preview: ECE 2704 Homework Number 1 Due at the start of class on 30 January 2008 1. Exercise 1.11 (page 138) (a), (b), (c), (d). In (a), assume the positive pulse starts at and ends at and that the negative pulse ends at . Make corresponding assumptions for (b) and (d). In (c), assume that the positive pulse starts at and ends at and that the negative pulse ends at . Solutions (a) (b) (c) (d) We note that negating a signal and timeshifting a signal do not appear to change the energy of the signal. Scaling a signal by 2 appears to increase the energy of the signal by 4. Of course, we could prove these conjectures more formally. For example, let the energy in a signal be . Let be a signal created by scaling by . Then the energy in is If , then the energy in the signal is unchanged. If , then the energy in the signal increases by four. 2. Exercise 1.16 (hint: to compute the signal average power, first compute the integral over one period) Solutions Since the nonzero part of the signal is infinite, the signal energy is undefined. To compute the signal power, first compute the integral over one period, Since the integral is not a function of , we can compute the integral over any multiple of periods and always get the same answer. Thus 3. Exercise 1.21 (page 141) (a), (b), (c) Solutions (a) 24 (b) 15 6 0 0 9 18 (c) 2 5 8 4. Exercise 1.22 (d) Solutions We do this in two parts. Let This yields and . Then 0 2 3 5. Exercise 1.41 (a) (b) Solutions 1 (a) (b) 5 7 1 6. Exercise 1.42 (a) (b) (hint: use the unit step function) Solutions (a) (b) 5 7 ...
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