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Unformatted text preview: Name: DLM’HD EEE 303: Signals and Systems Final Exam Lela}? S, EDDIE
Pref. PapendreeuSuppappela You meet answer all prebleme for full credit. The number of points for each part of a problem is given. .2" Fer full credit, show all steps end label ell axes. This area. is. for ofﬁcial use only: m... 1. Consider a. continuous time lines: timeinvariant [LTIjr system whose impulse response hit} and input signal ﬁt} are given by: 71?} 47(1) M1)
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, :11; l ‘9' : :f e 3. consider the LTI system mo} : Jain] — .7:[ri — 1] that corresponds to a discrete diﬁerentistor or ﬁrst—order diﬁel‘enoe ﬁlter. {a} {5 pts} Find and. plot the impulse response Mn] of the system.
{hi {T rats] Find the za—transforni {ET} H {s} of Mn] and provide the region of convergence {ROG}. {e} {8 pt?) If rho] = (sign she], ﬁnd the ET of yInbm provide the ROG. Does the disorete—time
Fourier transform of yin] exist? Why or who,r not? 51M”; Fiﬁ[v Us} “afnl: xiﬂ3ri‘iﬁmil
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I my ”I, Ht {5 Linc{UM ti W W 4_ Consider the following interconnection of corgisrﬂoustime LTI systems: [a] {5 pts} Find the overall impulse response Mn] of the system in terms of mks] for i =
1_. . _ . ,5 Note that no specific functions are to he used; your answer should he in terms of tile], habit. halo]. Mn]? hale]: hslﬁl {h} {5 pts) Find the metal] {requeuey response H {elm} of the system in terms of the discrete—time
Fourier transforms of hiin] for i = 1,. . . ,6. Your answer should he only in terms of Efﬁe“), Heidi Haidt Heels}, Half5W: HueF's). . _
{c} [Iﬂpts] Evaluate wajm(mi meat) hﬂn] = (31+ 1} (0.5)“ uln] hﬁn] = BCEEU.2H'H] Fight] = 5
huh] = leiM“ helm] = (0.2%an hsiﬂl = lﬂ4llxﬂ[Til ll .
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Mad} to ﬁlter“)  W”) + twister) + Hoot is a. You were asked to analyze Edge sinusoidal data :rft] = oos {wot} collected and sampled at a commu
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sinusoid. The following information was given to you: the data is stored inibtvariable x in It'facrtan5
the number of data points is N = 1024, if a}, = 4ﬂir then the decoded information is “Yes" and if
too = ﬁlh' then the decoded information is “No”. {a} (10' pts} Supposed you were told that the sampling period used was T = [m1 and that
Eflilo“ was transmitted. After loading the data in Manse using load 1:, {i} provide Marten
5’ commands to plot the data in the frequency domain with the axis correctly labeled in Hz, {ii} provide the resulting plot. {iii} what is the duration [in seconds] of your signal in time? .03
{b} {If} pts] Supposed you were told that the sampling period used was T ='&' and that the
“a transmitted information is W. Plot the corresponding MATLAB plot of the frequency domain
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 Spring '07
 Chakrabarti

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