EEN 340 Problems CHAPTER 5, Fall 2011

5.1 d. de™ sin(a@,t + @)u(t),b > 0 u= ety =sin(@,t + @) A at+ja@ — el®_@ a 270° 2j é 6 e [erode Seong 2y° 27 Aze!® F = ola — _ (@) 2ja-@ (@-@,) 2yb-0 Ae “u(t) = sin@= -jegt i 6 é Ame" d(@+@,) 5.8 use the derivate property a {a K\ 2. = FAQ Scle™ <3 qo (Bez) > (b) pany from Table 5.1 Fle) Se artes) By (A ae ee 5. (a\—?7 Ge) ave = Ee - ~32t @S 40s(at) _ 2fe?Set*| 24% 2e7 att t2+ | 2%1 e+ use Frequency: Shift and dualrty Properties -/W-2] Flo) = arf er e aie 5.12 (a) (i) He) = yr = ween (i) H@)|= Se LH(w) = —- tan71(#). See figure (below) for magnitude and phase plots. (iii) h(t) = 10e~!°"u(t) (b) () He) = some = zabr (ii) |H(w)| = za Tle ZLH(w) = —tan~!(w) (iii) A(t) = e~tu(t) part (3) |H4ooH{ part (0) |H(w , 7 AX 09 / \ 1 08 / \ 05) ss / \ 8 or / \ 0 / \ os} / x 05 me 05 Va NG 4 = 04 15 ~ -1 f) 1 2 2 4 0 1 2 o © Figure 2: Magnitude and phase of frequency response for 5.12 5.16 a (a-jt)* b) am X (we) - ls itty ée - i “ps ! _ ae. Anjo ALR aby es® 2) C) Sine (st) — __[~ 17 molt ph ietion properl - Fé HA re Q@) we Sampvep S/6WAL CAN BE WRiTTEN As Sale) = Ate) E S(e-nn) , = = BL = View Fas) = ge Fla) xe Z &sSlo-nw,) _ fn b) Ws = 200 (radg i's The Mygquist Frequenty for 7,lt) tus > 300 ( radl/. 15 netestary for Proper Sampling of- fy lt). 200 5.28 (a) P,(w) = P;(w)|H(w)|? H(150) — 8/200(150 — 100) + 16 — 18 H(200) = 8/200(200 — 100) + 16 = 20 P,(w) = (207)0.55(w + 200) + (18?) 26(w + 150) + (187)25(w — 150) + (207)0.54(~ — 200) Py(w) = 2005(w + 200) + 6485(u + 150) + 64856(~ — 150) + 2005(w — 200) co) 700 GHB 73a - 19d 10d “$0 8 90 150 (b) Py(w) = Ppw)|H(w)? H(—240) = H (240) = 21.6, H(—180) = H(180) = 19.2, H(—120) = H(120) = 16.8, H(—60) = H(60) =0 P,(w) = (21.62) [5(w +240) + 5(w—240)] + (19.22)[25 (w+ 180) +25(w—180)] + (16.8)(35(w-+120) +35 (w —120)] P,(w) = 466,56[5(w +240) + 6(w — 240)] + 737.28[5(w + 180) + 5(w — 180)] + 846.72[5(w + 120) + 6(w — 120)] Pylw) pete “lap “2° 4p “180