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Practice_final_soln

# Practice_final_soln - Name 1 Given the impulse response of...

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Unformatted text preview: Name 1. Given the impulse response of an LTI system hit) = siniEﬂattkeetﬂt) , determine the output 10 the fellewing three inputs. Label and sketeh the-eutput for all three mputs. Simplify yew answers as mﬁeh as pessibie. {25 points] lap?) :20!) = Mt} = sin{20m)reer(2t) SP4; Mt) = sin(2iint) 1 ire-ﬁt; e(t)=5{t)+5[t—E] lent. Glﬂﬁ Ink Name LL P 4‘ N11 u :15- ? ‘7 H5 5W 2. If a discrete version sf MI) {from problem 1] is desired, what would be a minimal ﬁnite sampling ﬁ‘equeney {Hz}? Justify your answer with some rough calculations. To make the math easier, you iris}.r approximate n = 3 ii'yau wish. Sketch and label a magnitude spectrum efyuur sampled signal. (15 points) sac-I‘M W": w: w s'm fazfa Q (r W1; 1 {c0 ..__———— r-—- 'E‘M/“F'g write; ‘3” we ([673 +25%. 92\$ /‘z’6‘ﬁ‘+ 10'5" apt/{est ... Geo/fee OLNEUM "hm,“aﬂr gﬂeéh’“ lDEQU (gml his: as“) be?” 3. Given the system diagram below, ifs“) = e"u(t), ﬁnd a suitable am and b(t)suel1 that the overall impulse response is am (I) = —c[t} . There may he more than one answer. {21} proﬁts] Name 4. Show that the Fuuriar Transfunn of a pulse train is anmher puise train. 1n lather wards, Show that: Z 50‘ — HT) <—>K Z 5(w— nwﬂ) Where “’9 = 2?” where K. is a constant. (2H points) ' 630 F5 .- tal? k} .. g *9 3”” pr an; \$5 LENA“ 4‘0‘)- (L J WEB Name 5. Design a digital FJR ﬁlter tn give the fellnwlng magnitude transfer function. The digital ﬁlter must have purely real coefﬁcients. Errata.r a block diagram fer the FIR ﬁlter. "What is the phase of the FIR ﬁlter at ﬁequeneyf = .125}; '3 {2D paints) DU nneae 0.125 0.1515 0.15 news EST! (1.4315 I15 %’ mew-nee w.r.t. re a ...
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