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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 theeutput 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 ireﬁt; e(t)=5{t)+5[t—E] lent. Glﬂﬁ Ink
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? ‘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) sacI‘M W": w: w
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(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}
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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 %’ mewnee w.r.t. re
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 Fall '07
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