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Exam1SolnSP12

# Exam1SolnSP12 - NAME 16 February 2012 EE301 Signals and...

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Unformatted text preview: NAME: 16 February 2012 EE301 Signals and Systems Exam 1 Cover Sheet Test Duration: 75 minutes. Coverage: Chaps. 1,2 Open Book but Closed Notes. One 8.5 in. x 11 in. crib sheet Calculators NOT allowed. This test contains two problems. All work should be done on the sheets provided. You must show work or explain answer for each problem to receive full credit. Plot your answers on the graphs provided. WRITE YOUR NAME ON EVERY SHEET. Prob. No. Topic(s) Points 1. Continuous Time Signals and System Properties 50 2. Discrete Time Signals and System Properties 50 t2 {W} — W — T1)} * H7105) — U0? — T2)} = 5 {MW — U0? — T1)} (1) 2 + (Tlt — {u(t — T1) — u(t — T2)} t2 T; — 3 Problem 1. [50 pts] Consider the LT I system characterized by the following I / O relation- ship: t W) = /,_1 and? (1) (a) Determine and plot the impulse response of System 1, denoted h(t), in the spaced provided on the sheets attached. (b) Determine and plot the output y1(t) in the space provided when the input to the overall system is the ramp-up triangular pulse of duration 2 seconds below. 3310:) = 2t{u(t) — u(t — 2)} (c) Determine and plot the output yg (t) in the space provided when the input to the overall system is the ramp—down triangular pulse of duration 2 seconds below. On the same page as the plot, express y2(t) in terms of y1(t). Note: 332(15) = \$1(—-(t — \$26) = -2(t - 2){u(t) — W - 2)} (d) Determine and plot the output y3(t) in the space provided when the input to the overall system is the rectangular pulse below: 2:305) = 4{U(t) - W — 2)} (e) The goal is to determine and plot the output y(t) when the input to the overall system is the signal \$(t) below. (i) Express \$05) in terms of xi(t), 2' = 1, 2, 3, defined in parts (b), (c), (d), respectively. (ii) Express y(t) in terms of y,(t), 2' = 1,2,3, your answers to parts (b), (c), (d), respectively. (iii) Plot y(t) in the space provided on the sheets attached. Input 33(t) Problem 2. [50 points] (a) For parts (a) and (b), consider causal LTI System 1 characterized by the following difference equation below. Determine and plot (stern plot) the impulse response MW of System 1 in the space provided on the sheets attached. System 1: 2 gym — 1] + — <—> x[n — 4] (b) Determine the output of System 1 when the input is the ﬁnite—length geometric sequence below. Plot y[n] in terms of a stem plot. ﬂﬂ[email protected]&Wd-Mn—M} (c) For this part and part (d), consider causal LTI System 2 characterized by the diﬁerence equation below. Determine and plot the impulse response MW of System 1 in the space provided on the sheets attached. System 2: = y[n — 1] + — \$[n — 3] (d) Determine the output when the input is the ﬁnite—length geometric sequence below. Plot in the space provided on the sheets attached. MM={MM-uW—N} (e) Consider that System 1 and System 2 are put in SERIES such that the output of System 1 is the input to System 2. Determine the impulse reSponse h[n] for the overall series combination and plot it in the space provided on the sheets attached. NAME: 16 Feb. 2012 Write your expression for h(t) and plot it, for Problem 1 (a) here. 1(b): For each value of 15, write the value of y1(t) in the table below. Range for t Linear Linear Quadratic Quadratic pos. slope neg. slope Concave Up Concave Down 0<t<1 1<t<2 )4 2<t<3 1(c): Write a simple expression for y2(t) in terms of 3/105). 1(c): For each value of t, write the value of y2(t) in the table below. Mark the correct box with an for each range for y2(t). Range for 25 Linear Linear Quadratic Quadratic pos. slope neg. slope Concave Up Concave Down 0<t<1 i l 1<t<2 l ﬂ 2<t<3 l X Plot y2(t) below. . A91 (4Q ~ La K < I I 1 Plot y3(t) for Problem 1 (d) here. 1 (e). Express 13(25) in terms of [El-(t), i = 17 2, 3. o< (J9) —— as 09> + x2 (#4) + N30c~1> 1 (e). Express y(t) in terms of yi(t), z' = 1, 2, 3. lam: Maw» waive-e Wyatt-ll You can use the plots below if they’re helpful for answering 1(e). 6 x l l l 7 Part (e). For each range of :5, put an X in the correct box in the table below. _l Range for 75 Linear Linear Quadratic Quadratic pos. slope neg. slope+Concave Up Concave Down 33:; ‘ X X L 2 < t < 3 _L Y 3 < t < 4 7/ Q r o T 4 < t < 5 l g X _l 5 < t < 6 X _‘ 6 < t < 7 7< For each value of t, write the value of y(t) in the table below. t W) t = 0 t = 1 t = 2 t = 3 t = 4 t = 5 t = 6 t = 7 Plot your answer mm to Problem 2, part (a) on this page. _L C). -N U1 |FII iilll‘ilillllli 0. O). . -|\3 U] l||||>llll 10 Show your work and plot your answer to Problem 2, part (b) on this page. 50 _ ‘ 45- f. . HA1}, 4o— 3 ' 30— 25-. . . , ;\ 20- 11 Show your work and plot your answer mm to Problem 2, part (c) on this page. IIIiIiLIIIIIIII I I" I l I I l I I I I I I I I 0W Inca : we MEN'S {X amhke of A6 CK)"— 0‘\ AgCIA’D ‘\" 'X Ch] ~0L® xch—Dj WHK 0L:\ th‘ \ ‘gor a“ VI 9 7 H (1? (I 12 Show your work and plot your answer to Problem 2, part (d) on this page. 13 Show your work and plot your answer h[n] to Problem 2, part (e) on this page. 14 ...
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Exam1SolnSP12 - NAME 16 February 2012 EE301 Signals and...

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