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# Signals and Systems ECE 314

UNM

GPA 3.99

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This 6 page Class Notes was uploaded by Roel Green on Wednesday September 23, 2015. The Class Notes belongs to ECE 314 at University of New Mexico taught by Staff in Fall. Since its upload, it has received 20 views. For similar materials see /class/212172/ece-314-university-of-new-mexico in Engineering Electrical & Compu at University of New Mexico.

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Date Created: 09/23/15

ECE314 Summer 2008 EXAM I Review Questions 1 A linear timeinvariant system has the inputoutput characteristics shown in the rst row of the diagram below Determine the output for the input shown on the second row of the diagram Justify your answer input x1 n outputy1n Solution Note that x2n x1 n1 05 x1n 1 1 As a consequence of the system being LTI we must have yzny1nl05 y1n Then you n 71 input MM output ydn can sketch 1t ea51ly 1 I H O O 0 5 n n 2 Consider the signals t utut l and gt ut a Sketch Zt and t 05 Solution zt I05 l i E t 05 I 05 15 b Sketch 05t gt Solution 1 11054 f05tgt 1 05 05 05 3 Consider the signal g shown above Is it periodic If so what is the period Is it a power or an energy signal If it is an energy signal calculate its energy and if it is a power signal calculate its power Solution The signal is periodic with period N3 since gnNgn for any 71 Since it is periodic it must be a power signal and not an energy signal E is in nite P131102534 4 Evaluate the following quantities by inspection a J coss5s 4ds no 2 5 Consider a system described by the following inputoutput relation ya utxe39 a Is the system linear Justify Solution No If we choose x30 then ytut9 0 b Is it time invariant Justify Solution It is not time variant Use the time invariant de nition to prove c Is it memoryless Justify Solution No because y0 depends on xl d Is it causal Justify Solution No because y0 depends on xl 6 Determine whether the following systems are stable you must show proper justification ie provide a proof in the case of stable and a counter example otherwise a ya glows Solution Take xt ut which is bounded by one Then yt usdS tut And lytl ltlut which is unbounded Thus the system is not BIBO stable b yn l 3xn l xn xn 1 Solution Assume x is bounded by M Then l yn ls l3M M M 3M which is bounded The system is therefore BIBO stable 7 Suppose that the systems in Problem 6b is linear and timeinvariant Calculate its impulse response Simply replace x by 5 to obtain hn l36n l 6n 5n 1 Once you mastered these questions try to work the next set of question Let me know if you have any questions next page Review Questions Set 2 l A linear timeinvariant LTI system has the inputoutput characteristics shown in the first row of the diagram below Plot yzt Justify your answer and clearly mark the axes as needed input x10 output MO 2 1 1 1 2 t 2 t input x20 output yzt 05 2 t t 2 a Is the system described in Problem 1 causal Justify your answer b Can you say if it is stable or not Justify your answer c Graph x1t l x12t x105t and 2y1t6tl E a Graph g2n b Is g it periodic If so what is the period Is it a power or an energy signal If it is an energy signal calculate its energy and if it is a power signal calculate its power 4 Evaluate the following quantities by inspection a f 4550 sds b mm c 240 5n k sinz 2k 5 Consider a system described by the following inputoutput relation ya xt a Is the system linear Justify b Is it time invariant Justify c Is it causal Justify d Is it stable Justify

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