A#12_Solutions - Assignment #12 — p.1 ECSE-2410 Signals...

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Unformatted text preview: Assignment #12 — p.1 ECSE-2410 Signals & Systems — Spring 2009 Due Fri 03/06/09 1(32). Speech scramblers are designed to prevent electronic eavesdropping. The input voice, x(t), is 1— i"— {w| < 1000 made unintelligible by altering the original spectrum, X (0)) = 1000 ’ — . The garbled output 0, else y(t) is then transmitted to a receiver at the listening end. The receiver (not shown) sequentially undoes all the frequency spectrum alterations done at the transmitter. Hi h ass Filter Low ass Filter 2 -Eg a i i : (d)(8).; Sketcizh mg) andilabel an important points. 9 i i i i z i i i Z a i ; i a :5 :3 e l x(t) , Y“) T —2000 0 2000 —1500 0 1500 cos(2000t) cos(3000t) For the transmitter filtering operations shown in the block diagram above, sketch (a)(8). Sketch A(w) . Show all amplitudes and frequencies. Label all axes. an"? : é g a 3 {A} X raw (b)(8).§ Sketizh B( and, labelg the aE es. : i r i i 2 3 3 i t i E 3 3, 3 é : t i i 3 z 7, g i ' g g g a i as g i g 5;) X Egg? g i 2 é “:3 a? g ' (0(8); Sketéh C(ég) andiiabeigau iniportaéit points. i E i a - 5 2 i r i 2 2 i E z § § i E i a i in awe § E i E“? i : i E E @gigfle i : i E Assignment #12 - p.2 ECSE-2410 Signals & Systems - Spring 2009 Due Fri 03/06/09 2(36). In this problem we use a nonlinear (squaring) circuit element to “modulate” a carrier signal, C(t) = cos(8t), with the amplitude of the input (or modulating) signal, x(t). In effect, the amplitude variations of the low frequency (160! S 2) audio signal, x(t), is “transferred” to the amplitude of the high frequency (a) = 8)carrier signal, C(t). Consider the system, x(t) 1M (0) l 2 a) *2 C(t) = cos(8t) _ 7rd} ‘ where C(t) = cos(8t), and the Fourier transform of MP) is Sgwa 598%, (a)(26). Sketch B(a)), the complete spectrum generated by the nonlinear device. Label and scale all values and frequencies. his == fa: :- ffiefi crystal) a firearm aoségélat» 1; flaw filkw‘xgjw fiflfilfflw) :7» at 5.255%? wfiffiflél” 2&3“ Eggéwdaééwefl: E (ma-'3‘; +Eiw+3§ 3, firm”? “é””"¥”'”’” r’nrr“, g E i r g g 2 MW Wm , ,waméwawawawiwrwu f , i i g t r 2 E , g = r l § § é % g , 77 7 .mwwéw.? g ' i 2 g r r : ' i E s V T a 3 i a} c 2 é % , i E 4% ~F§2~Ziei8, ' é E‘q‘éfléi é : i 2 g r a 2 r z i .2 r z t é, ; g (b)él&). Sketch Y2 w§,t e spectrum of the d Sire modalatedmgnazl, after frl r % E a g r g i i i s s g a E é '2 E g z t 2 r z 3 a a 2 fl z 3 r E z E g r E é z E i i; E i " Due Fri 03/06/09 Assignment #12 - p.3 2410 Signals & Systems - Spring 2009 Transmission channel (0 x20) 3(32).Two telephone conversations, x10), x20) , are sent over the same telephone wire and recovered at x the receiving end telephones. (a)(10).Sketch W(w). Label all frequencies and amplitudes. ECSE— w? 5 § z E sketch A A s E 9 % 0V? 2 i 3 i £11, £50) she ; a i ;wn ab ; é anwéwg E i 2( B 3’ g 5 i '% 5% i. rm is is i s .. t K . ,E . , . ; a s: t s: s: s; :2. W: E ,5 ...
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A#12_Solutions - Assignment #12 — p.1 ECSE-2410 Signals...

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