Quiz 2 Solution

# Quiz 2 Solution - 8&(Vb‘ll‘0‘4(SC MFJ €FM Name...

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Unformatted text preview: 8&(Vb‘ll‘0‘4 (SC MFJ+€FM Name: Student Number #: City University of Hong Kong E Department of Electronic Engineering if: EE 3210 Systems and Signals Midterm Quiz 2 NOTE: 1. 1. This is a 1.5-hour, open book, open notes midterm test. 2. There are 4 problems altogether, which amount to 20 points. 3. In addition to ﬁnal answers, you need to include necessary steps to show your derivations. An 1/ answer without any supporting development will unlikely be awarded with a point. You do E receive partial credits if you write down the steps despite that you may not complete your 3 solution. ' 4. Write your work in the blank space. If necessary, write on the back sheet. _ E; 5. Enjoy the test, and good luck! 1. (4 pts) Suppose that a:(t) is a periodic signal with a, fundamental period Tm. Let y(t) = :1:(—at + b), a > 0. ‘ Show that the exponential Fourier coefﬁcients for y(t) are given by 311: = z—ke’jm’b. Where w; = 27r/Tz, and an; are the exponential Fourier coeﬁicients for \$(t). ALSW'AK (Ike-u: *5 Maxi! Werh‘m Pros? 0g ﬁx: .ren‘m.) W 3’ Scl' ”0.7:? 2-7}, ;‘,€./ ﬁm‘i This ‘jét +75) = M; cure—72¢) : “(4%):94). 3+ Mm ”(VJ _. - 21L 2H an W ”3'1’7157*a1=“”‘ :5 s) e W D . ’Pd—lo Mr T‘s-attic /,0>J6r2<[’03 a’dhw‘ “A (-7004? (-1) K T« {if _, ,3'lewﬁlg L] A «<1(’/‘)"J%T _\ ( P ,, g, T)‘ Radclé. dc W —Ohuxb «vk it 2. (6 pts) Consider a LTI system with frequency response . jw + 1 HQ“) - W (i) Determine a. diﬁerential equation that describes the system. (ii) Find a block diagram realization consisting of adders, integrators, and coeﬁicient multipliers for this system. (iii) Suppose that an input signal m(t) = e'ztu(t) is applied. Determine the output response. ' Solut'o’m: 1 . ) . ﬂ "‘ 3% “WWW” >> Mme 17w yaw) +12 W) 45%;») MM (“V-e, Mt, yaMﬁ’m: 13%;)” J96)+}7,5G) 559%“) 5”“ Nu.) . . ‘ -- L' Wad) =H(ow) We”) ’-' W) . // ‘131.\.‘1.‘\.u.‘1‘\.1.1“.‘1f1'uhNv'w ((5) ’ 8+1 + 5&5 + Wk 3 : 8+2) (0‘ iii-- ,L 3: A C Y ”2 («BWWM‘ 27.1 x: 2N5 l 3H 3 Q , ’ 2 ‘ 75 (“9)“) 5,—2, * Cgfzy(\$+¢lv)\s='3 Z 8“" ﬂ 3 § C , aswwsvlw s @5157?“ E * \ wace/ ‘ 1 l / 4/ ‘ (Ft mow £316 ”a“ 50”” 5K (5 pts) The Fourier transform of a certain signal a:(t) is given in the following ﬁgure. Find z(t) without performing any integration. ' 4. (5 pts) A continuous-time system is determined by the following integral-diﬁerential equation (ZZZ/(t) dt2 + 3y(t — 1) +/o1t y('r)dT—- — that) — :c(t), which relates the input 2(t) to the output y(t). Find the transfer function H (jw) for this system. So [wtma A {Pf (c1960? :0”) Y9» ‘3”){11’ 2(9) :GLJJXHM) I,“ :{w-nﬁ : (WM ...
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