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solution6

# solution6 - ECE 101 Linear Systems Fundamentals Problem Set...

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ECE 101 – Linear Systems Fundamentals Problem Set # 6 Solutions December 1, 2009 (send questions/comments to [email protected]) Speed Problems 9.1 a. b. c. d. e. f. Note : In e. and f., we use the fact that 9.3 The ROC is given by .

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x(t) is a sum of two signals. The ROC of the first signal is }. The ROC of the second signal is }. The ROC of the sum is atleast Therefore for the ROC to be we need to have and there is no restriction on the imaginary part of β . 9.6 A. Since x(t) has a pole, it cannot be of finite duration. B. Since x(t) has a pole at 2 and it is absolutely integrable (ROC includes the imaginary axis), its ROC cannot be right sided. Hence x(t) could be left-sided. C. x(t) cannot be right-sided as reasoned in B. D. x(t) can be two-sided, if it has atleast one more pole on to the left of the imaginary axis. 9.10 A. The poles are both on the real axis. If we move on the imaginary axis starting from the origin, the denominator of the transfer function will be smallest in magnitude at the origin and increase monotonically as we move away from the origin. Thus the magnitude of the
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