ESE-2018 PRELIMS TEST SERIES Date: 12 th November, 2017 ANSWERS. 61. (d) 121. (c) 2. (a) 62. (a) 122. (b) 3. (b) 63. (a) 123. (c) 4. (b) 64.
|
|
- Dana Lloyd
- 5 years ago
- Views:
Transcription
1 ESE-8 PRELIMS TEST SERIES Da: h Novmbr, 7 ANSWERS. (d). (a) 6. (d) 9. (d). (c). (a). (c) 6. (a) 9. (d). (b). (b). (a) 6. (a) 9. (a). (c). (b). (b) 6. (a) 9. (b). (a) 5. (d) 5. (c) 65. (b) 95. (a) 5. (c) 6. (d) 6. (c) 66. (a) 96. (b) 6. (d) 7. (c) 7. (d) 67. (b) 97. (a) 7. (b) 8. (b) 8. (b) 68. (b) 98. (a) 8. (a) 9. (c) 9. (b) 69. (d) 99. (b) 9. (c). (d). (a) 7. (c). (c). (a). (b). (c) 7. (b). (c). (c). (c). (b) 7. (b). (d). (a). (a). (c) 7. (b). (d). (b). (b). (b) 7. (b). (d). (b) 5. (a) 5. (b) 75. (b) 5. (b) 5. (c) 6. (c) 6. (b) 76. (c) 6. (d) 6. (b) 7. (b) 7. (d) 77. (a) 7. (c) 7. (c) 8. (a) 8. (b) 78. (c) 8. (b) 8. (b) 9. (d) 9. (a) 79. (c) 9. (c) 9. (c). (c) 5. (c) 8. (b). (a). (c). (a) 5. (a) 8. (b). (b). (c). (d) 5. (b) 8. (a). (b). (b). (c) 5. (a) 8. (b). (b). (b). (b) 5. (b) 8. (c). (a). (c) 5. (a) 55. (b) 85. (c) 5. (c) 5. (d) 6. (a) 56. (a) 86. (d) 6. (b) 6. (c) 7. (a) 57. (d) 87. (b) 7. (a) 7. (b) 8. (b) 58. (b) 88. (b) 8. (b) 8. (c) 9. (c) 59. (d) 89. (c) 9. (c) 9. (a). (b) 6. (c) 9. (c) (c) 5 (c)
2 () (Ts - 8)- Novmbr 7. (d). (a). (b) VLF ( o Hz) SONAR VHF ( o MHz) Air Traffic Corol SHF ( o GHz) Salli commuicaio MF ( o Hz) Mariim radio (A) o Hz (LF) Navigaio (B) o MHz (HF) Tlgraph (C). o GHz (UHF) Wird lvisio (D) o GHz (EHF) Radar Hr,. (b) 5. (d) 6. (d) B 6 Hz SNR Chal capaciy C B log ( + SNR)bis/sc C 6 log ( + )bis/sc 6 log bis/sc 6 bis/sc Daa ra ( 6 bis/sc) > chal capaciy Daa rasmid will hav rrors. Hr, chal capaciy C 56 bis/sc Now, C B log ( + SNR) bis/sc (SNR) db db log SNR SNR B C log ( SNR) 56 log 8.5 Hz All h hr sams ar corrc. Modulaio is usd for frqucy raslaio, Muliplxig rducig aa high ad covrs wid-bad sigal o arrow bad sigal. Wh modulaio idx i AM is grar ha, h vlop is disord ad dos o coai acual mssag. 7. (c) 8. (b) 9. (c). (d). (b). (c). (a). (b) For a SSB-SC, h badwidh of modulad sigal is qual o B.W. of mssag sigal Opraio of muliplyig a sigal wih siusoidal sigal is calld Mixig or Hrodyig m() A cos For o vlop disorio c A m()cos c c c K m(), ls h modulad sigal dos o coai acual mssag sigal. If f c < Mssag sigal badwidh, h modulad sigal will coai ovrlappig sidbads. I-phas compo dpds iry o mssag sigal Quadraur compo irfr wih h I-phas compo o rduc or limia powr i o of h sidbads dpdig upo how i is dfid. Quadraur compo of modulad wav is a filrd vrsio of mssag sigal ad is usd o limia o of h sidbads hrby modifyig h spcral of modulad wav. s() A m()cosf c c a A cosf y() A m()cosf A cosf c c c c y() A [ m()]cosf c AM sigal (Ka ) V max V, V mi V Modulaio idx c c c y() Vmax Vmi.5 V V max mi Hr, V max.5 V ad V mi.5 V Modulaio idx Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
3 (Ts - 8)- Novmbr 7 () 5. (a) 6. (c) 7. (b) V V max max Hr, f c + f m 55 f c f m 5 f c V V mi mi.5 (.5).5 (.5) Hz Am Modulaio Idx.8 A 5 c (raio of mssag sigal volag of carrir sigal volag) Toal powr P LSB A c m R 5 (.8).65 W P USB m A c 8R c A Toal powr P T P T 8 6 Modulaio fficicy A c m R 6 W 8. (a) P SB P T.% m P T PC 9. (d) P T P C.89P T (.5) PC 89% is carrir powr ad hc % is sidbad powr. m Toal powr i AM P T PC As m icrass P T icrass P C. (c). (a) A c R m P T Pc P c P c idpd of m 5. A c R A c. 8.6V Pa ampliud of carrir afr modulaio A c ( + m) V max V V max A c ( + m) V V mi A c ( m) V V max + V mi A c + A c m + A c A c m A c V max V mi 7V Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
4 () (Ts - 8)- Novmbr 7. (d) I C 8A ad I T A m I T IC m 8 Giv o K Effciv ois mpraur of h rcivr T (F ) To F log T ( ) K Th ovrall ffciv ois mpraur. (c). (b) m.565 m.5.6 s() [.cos( ).8 si( )]cos( ) m. ad m.8 N modulaio idx m 8 m m (.) + (.8).8 Modulaio Efficicy m m % m.8 s() [. si( ).cos( )]cos( ) Hr, m., m. 5 9 m m m...5 P T P T Also, 5. (a) m A c m PC R (.5) 5W f Hz ad f Hz m m Badwidh Highs frqucy compo of mssag sigal 5 Hz Hz DSB wih carrir or AM wav ca b grad usig: (i) (ii) 6. (a) Squar law Modulaor Swichig Modulaor 5 T IN T a +T + K Ovrall ois figur 7. (a) 8. (b) 9. (c). (b) F T T IN o F db log db For a bad-pass sysm, miimum samplig frqucy f s whr K f H K fh fh f L fh 8 fh f L.5 f s MHz 8 I Mid-ris quaizr, ipu valu bw ad is mappd o a oupu valu of.5. For X() o b saioary µ x () mus b idpd of i.. x () E[X()] E[P] si + E[Q] cos mus b idpd of which is possibl oly if x () E[P] E[Q]. Givh() u() h(f) F T [h()] jf Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
5 (Ts - 8)- Novmbr 7 (5). (a). (c) so,s y (f) S f hf N f x Auocorrlaio fucio R y Ivrs F.T. [S y (f)] y R F N N f For a uiformaly disribud radom variabl W hav variac E X EX Ma µ x E[X] b a x f x dx a b x dx b a ad E X b So E X EX a x x dx b a b a b a, hr b 5 ad a So 5.75 b a Lmpl-ziv codig schm dos dpd upo sourc saisics, hc i is uivrsal codig schm.. (b) h(x) log dx log dx log log Muual iformaio of a BSC is I(X, Y) H (Y) + p log p + ( p) log ( p) which is maximum wh H(Y) is maximum. Maximum H(Y) is achivd wh ach oupu has probabiliy of.5 ad H(Y) max So chal capaciy of BSC C s 5. (c) 6. (c) 7. (d) max I (X, Y) + p log p + ( p) P(x) log ( p) I a bloc cod d mi, h miimum disac bw ay wo cod words of h cod is ( + ). cod r of a (,, L) liar covoluio cod rpas afr (L + ) h sag. Fro a raisd-cosi spcrum Badwidh B W R b WhrW T Giv,R b 8 Kbps b. (a) Diffrial ropy of a coiuous radom variabl is giv as h(x) Hr f x (x) f x(x)log dx f x(x), K x K, ohrwis 8. (b) W 8 KHz Badwidh KHz Giv Log i log P P I ca b wri as i LogPi i logpi i Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
6 (6) (Ts - 8)- Novmbr 7 Muliplyig by Pi ad summig ovr i yilds m m m P log P P P log P...() i i i i i i il i i m m m i i i i P log P Pi log P P H X i i i 9. b. a Thus q. () rducs o H(x) L H X Giv () c()cosc s()si c vlop E() () ad c variabl s c s () ar idpd radom So E() has rayligh dsiy Th oupu of rcifir is giv by x( ), x( ) -x, x( ) y( ) Th probabiliy dsiy fucio of guassia procss is x f ( ) x ma x f ( ) x x f y( ) y x x y( ), x( ) y( ), x( )< dx fx x y fx x y dy dx dy fy y y y / dx dy y /. c W hav s C Blog N s Blog B N B Wh B lim B C lim B B x. b powr spcral dsiy of ois s Blog B s B s lim log s B lim x log x log. Hc lim C s. B Erophy H P log log log log P i i i 9 7 log 6 log 9 log log. bis Mssag Prob m y y m y y y m y y y 9 9 m y y 9 9 m y y m y 6 7 m y 7 7 y -ary cod Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Avrag lgh Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
7 (Ts - 8)- Novmbr 7 (7) L 7 Pi Li i bis. c. b 5. b Efficicy H % L. %. % Giv BW of sigal f m 8Hz Nyquis ra f s,mi f m 6 Hz Samplig ra.5 Nyquis ra fs.5 6 Hz If umbr of bis i a word ar h umbr of quaizaio lvls Iformaio ra f s bps Sic fucio is dfid as sic (x) si Hc f() x x si si Nyquis ra is drmid by highs badwidh/frqucy compo. For sic () highs fq 5 Hz For sic () badwidh Hz Hc Nquis ra Hz Prs SNR db Dsird SNR db Hc, a icrm of db Sic icrasig by o bi rsuls i 6dB icras i SNR. So, o hav db icrm i SNR, w d o icras by Dsird + 6. b Fracioal icras i rasmissio badwidh % % I PCM, h B.W. rquirm f m whr o. of bis 7. d 8. b 9. a Quaizaio lvl icrass from o 6 mas o bis o bis BW fm BW fm (BW ) doubld Giv f m KHz f s KHz (Nyquis ra) L 5 bis Bi Ra KHz 5 bps For a raisd-cosi puls, daa ra is [B Bad widh 5KHz] B R b T 5 56bps.5 For a raisd cosi pulss B Hr w hav T b. R b 6 H T b B KHz.Mbps T 6 b 5 scod B T b z Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
8 (8) (Ts - 8)- Novmbr 7 5. c 5. (a) 5. (b) B T b 5 6 (Idal low pass filr) S For a PCM sysm giv Nq db or or L q db,mi S N L L or L Drawig h TTL om pol NAND ga as show blow ad applyig ipus A, B, A B E R B C E Q ON V CC R C B OFF Q D Q R Q ON o/p y C OFF For NAND ga o/p y for ipus A, B. I ordr o hav o/p y, Q should b i OFF sa. This will happ bcaus whvr Q ON h bas of Q is o forward biasd hc. Q is OFF. Wh Q is OFF Q bcoms ON as bas of Q is forward biasd as Q is ON curr flows hrough h capacior C ad gs mos chargd o V CC hrfor boh sids of h diod hav volag ad diod D gs rvrs biasd ad hc Q bcoms OFF. Sam I is ru bcaus i cas of rippl 5. (a) 5. (b) 55. (b) addr (or) paralll addr hr is propagaio dlay i carry from o flip-flop o ohr. Sam II is fals bcaus his propagaio dlay i carry is rducd by usig carry loo ahad addr. MUX-Srial o paralll covrsio DEMUX - Paralll o srial covrsio FULL ADDER - 9 NAND gas ar usd. Carry loo ahad addr - Rducio i carry propagaio dlay. W ow ha from absorpio law x xy x y x xy x y Proof : 56. (a) x xy x xx y [From disribuio law] Hc provd. () (x + y) ( x x ), By Complimaio law (x + y) So absorpio law is usd i sp (). From h giv circui diagram For o/p Y 5. Hc LED 5 will b forward biasd ad glow. For o/p Y. Hc LED will b forwards biasd ad glow. For hr is o valid oupu hc o of LEDs will glow. ( 9) +9 For gaiv Sig Now, s complm form of 9 is producd by aig s complm of +9 s complm : 's complm of +9 s complm : + s complm of 9 is. Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
9 (Ts - 8)- Novmbr 7 (9) 57. (d) Numbr of Boola xprssios havig variabls Hr, 58. (b) 59. (d) h 8 56 F A B. A B Applyig D Morga s horm Th, F. (A) A.B AB A.B. A.B AA.BB A BA C AA BA AC BC (B) BA AC BCA A BA BCA AC BCA AB C AC B AB AC A B A C AA BA AC BC (C) (D) 6. (c) Sac : A B AC BC A AC BC A C BC A BC AB AC BC AB AC BCA A AB ABC AC ABC AB C AC B AB AC A BA CB C A BA CB CA A B ACA AC AC AB 6. (d) I is a R/w mmory rsrvd for sorig iformaio mporarily. EI (Eabl irrups) MVI A, 8 H A -8 H SOD SDE R 7.5 MSE M 7.5 M 6.5 M 5.5 Srial R 7.5 is o availabl oupu Daa ON as No availabl i is Srial daa abl Hc all h irrups RST 7.5 RST 6.5 ad RST 5.5 ar abld. 6. (a) Idxd addrssig mod of addrssig is vry usful for arrays. This addrssig is o prs i microprocssor 885. Th 5 yps of addrssig mods prs i 885 ar. (i) 6. (a) Immdia Addrssig Mod: A immdia is rasfrrd dircly o h rgisr.eg: - MVI A, H (H is copid io h rgisr A) MVI B,H(H is copid io h rgisr B). (ii) Rgisr Addrssig Mod: Daa is copid from o rgisr o aohr rgisr.eg: MOV B, A (h co of A is copid io h rgisr B) MOV A, C (h co of C is copid io h rgisr A). (iii) Dirc Addrssig Mod: Daa is dircly copid from h giv addrss o h rgisr.eg: LDA H (Th co a h locaio H is copid o h rgisr A). (iv) Idirc Addrssig Mod: Th daa is rasfrrd from h addrss poid by h daa i a rgisr o ohr rgisr. Eg: MOV A, M (daa is rasfrrd from h mmory locaio poid by h rgisr o h accumulaor). (v) Implid Addrssig Mod: This mod dos rquir ay oprad. Th daa is spcifid by opcod islf.eg: RAL CMP. ALU prforms arihmaic ad logic opraios. Thr is o sorig lm i Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
10 () (Ts - 8)- Novmbr 7 ALU. Th oupu dpd o h curr ipu o ALU. I has irly combiaioal circuiry. 7. (b) A B A AB A B 6. (a) I mmory mappd I/O MEMW or MEMR sigals ar usd as corol sigals. B AB A B F 65. (b) 66. (a) 67. (b) 68. (b) 69. (d) B C 7. (c) Daa bus is a bidircioal bus. Th daa flows i boh h dircio bw MPU ad mmory ad priphral dvic. Addrss bus is a uidircioal bus. For xpadig 6K 8 o K 8, h rquird 6K 8 RAMs ar, 6K 8 8 6K Sofwar Irrups : RST;whr,,,,, 5, 6,7. i.. RST : RST, RST, RST, RST, RST 5, RST 6 ad RST 7. Hardwar Irrup : TRAP, RST7.5, RST 6.5, RST 5.5 ad INTR Poi P is suc a C B Th, Z W f A P X BC Y BC A Z A W f A X BC, Y X BC BC. A. A Th oal o. of ar (b) 7. (b) 7. (b) 75. (b) F A BA B AB AB A B A B EX-OR ga Th oupu of NAND ga is ABC A B C Y A A B C C A B C Which is h oupu of opio (b) Y ABC A B C Sic, A A ad, A A So, A A A A A A CD AB F BD CD ABCD d Giv is a sychroous cour, o. of FF Truh Tabl : CLK Q Q Thus mod- cour. Hc K. d d Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
11 (Ts - 8)- Novmbr 7 () 76. (c) 77. (a) 78. (c) 79. (c) CLK bi modulo-6 rippl cour No. of FFs Miimum im priod of o cloc puls 5 sc. sc. Maximum cloc frqucy 6 5MHz Cas : Wh Q D Q T Q + (Rquird for D FF) Cas : Wh Q D Q T Q So, T D Q DQ + DQ (i.. Q ) (i.. Q ) (i.. Q ) (i.. Q ) i.. rquird ga is EXOR ga. S R 8. (b) Th maximum cloc frqucy Hz MHz Hz pd(ff) 8. (b) 8. (a) 8. (b) Frqucy of oupu 8 T 8sc. f 8 CLK QA QB QC QD QB QD 5 6 Afr 6 cloc pulss, h oupu is rpad. Th oupu of EX-OR ga is h ipu o D flip-flop D Q I Q I As I is s high D Q Q Q I D flip-flop Q + D Q + Q Q Th umbr of flip-flops rquird o ma a modulo rippl cour log log () f max pd Th oupu of dividr 6 6 Hz Th Johso cour will ma h oupu 8. (c) pd f max 6 sc. frqucy Hz 8 Th Schmi riggr dos chag h frqucy Y AB A B AB A(B B) B AB AB AB B Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
12 () (Ts - 8)- Novmbr 7 B AB B 85. (c) AB.x.x.x (d) 87. (b) 88. (b) 89. (c) x x x + x 5 x 7, 7.5 x 7 ax x ca o 7.5. A B Bulb OFF ON ON OFF Th abov ruh abl is sam as ha of EX-OR ga Y AB AB. f W WZ ZXY W( Z) ZXY f W ZXY Th abov xprssio of f shows ha ga No. is rduda. Toal 5 NAND gas ar rquird o implm X Y 9. (c) 9. (d) F Y XZ. From h ruh abl i is ifrd ha h oupu is high wh boh h ipus ar sam ad i is low wh h ipus ar diffr V V av 5V ; ; T / ; T / T / ; T / T T T 5 5 T 5T 5 T T V av Oupu of ga, Y x x T/ F XY XYZ XY(Z Z) XYZ XYZ XYZ XYZ Oupu of ga, Y x x + x Oupu of ga, Y (x x + x ) x x x x + x x Oupu of ga, Y x x x + x x + x Oupu of ga 5, Y 5 (x x x + x x + x ) x 5 x x x x 5 + x x x 5 + x x 5 Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
13 (Ts - 8)- Novmbr 7 () 9. (d) Hc f x x x... x + x x x 5... x x + x FFFF 5AB A5E A5F i.. Y High oly of A B i.. ihr A, B or, A, B So, opio (b) is corrc. 95. (a) So, F s complm of (5AB) 6 (A5F) 6 9. (a) 9. (b) Giv, X (X) (.) 6 Sic, 6 7 () 6 To ur off LED, oupu of NOR ga should b high. Oupu of NOR ga, Y AB AB AB AB AB A B A B A B AA BA AB BB AB AB A B 96. (b) 97. (a) A K - map. : Q J Q K Q Hc afr h arrival of h cloc dg Q ad Q. For NOR lach B C D Prvious sa ivalid sa Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
14 () (Ts - 8)- Novmbr (a). (c) If propagaio dlay for o FF FF h, h for -bi cour; propagaio dlay for Sychroous cour, FF.sc. Rippl cour, FF.sc. i.. opio (c). (d) 99. (b) (Q, Q ) is,,,,,,,.... (c) [SOLN] Truh abl of J-K FF : J K Q Q Q.(d) Truh Tabl of D-FF : D Q Truh Tabl for h abov circui, D CLK D Q Q Q Q Q Q Q i.. opio (d) y() x() * h() or y() h( ) X ( ) d... Igraio x( ) im shifig i.. Q + JKQ JK JKQ A A B Q A A B A A B Q ABQ AB ABQ B AQ AQ AB B A Q AB.(d) h( ) x( ) muliplicaio Giv y[] x[] x[ ]...() y[] A [] [ ] [Puig h valu of x() i q ()] y[] bcaus [ ] ; Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org [] ; ad Sic y[] dpd o pas valus so i is o mmorylss.
15 (Ts - 8)- Novmbr 7 (5) 5.(b) Sic y[] for all valus of so i is o ivribl. L x () cos( )[u( ) u( )] () & x () u() () & y() x () * x () y() x ( ) x ( ) d 6. (d) H H 7.(c) () Puig h valus from q. () ad q. () x ( ) cos( )[u( ) u( )] () x ( ) u( ) x ( ) for < ad > + y() for < < So from q. () y() y() x ( ) cos( )d si( ) si( ) ohrwis (5) I is causal bcaus h oupu dos o appar bfor h ipu. I is o causal bcaus h oupu appars a, o im ui bfor h dlayd ipu a +. Sic o pol li i righ half of s pla so fial valu horm is o applicabl. Giv impuls rspos is causal h ROC Img 8. (b) 9. (c) H(s) s (s ) (s ) Usig parial fracio H(s) A B s (s ) By solvig, w g A ad B H(s) s (s ) By aig ivrs laplac rasform, w g h() u() H( ) + h( ) For causal h() for < For saic rasfr fucio of h LTI, sysm should b idpd of frqucy ad aur of impuls rspos should b impuls a origi which is valid for opio (c) oly. S () (7) si() s () xp ( 7) si ( ) No priodic Ral S () cos + cos + cos 5,, 5 Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
16 (6) (Ts - 8)- Novmbr 7 T, T, T (a) a T, T, T 5 x() ( ) d (hr a ) T T. (a). (b) raioal Similarly, is priodic T T, T T ar also raioal. So S () S j8 is also priodic wih frqucy 8 rad / sc Giv y[] u[] u[] y[] x [] * x [] y[] x [] * x [ ] y[] u[] u[ ] u[]...() u[ ]...() from () ad () y[]... u[] im u[] for y[] ( + ) y[] (+) u[] Giv, x() ( ) d.(b) if h oly ( ) is dfid For, ( ) x () ( a)d x (a) ( a) x() x() x() x() ( )d ( )d FT cos X(j ) [ ( ) ( )] F.T h() H( j ) y() x() * h() F.T 5 () j y() Y( j ) H(j )X(j ) By puig h valus from quaio () ad quaio () Y(j ) 5 [ ( ) ( )] j ( ) ( ) ( ) ( ) 5 j j x() ( ) x( ) ( ) ( ) ( ) Y(j ) x() [( ) d ( ) ( ) 5 j j Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
17 (Ts - 8)- Novmbr 7 (7). (b) ( ) ( ) + 5 ( ( ) ( )] + 5 j( ( ) j( ( ) j ( ) ( ) IFT Y( j ) y() si() Taig fourir rasform of giv diffrial quaio (j ) Y(j ) + (j ) Y(j ) + Y(j ) (j ) X(j ) + X(j ) Y(j ) [(j ) + (j ) + ] X(j )[(j ) + ] Y(j ) X(j ) j (j ) (j ) Th frqucy rspos is ( j ) H(j ) (j ) (j ) H(j ) A B (j ) (j ) j (j )(j ) O solvig valu of A / ad B, w g H(j ) j j Taig ivrs fourir rasform of H(j ) y[] x[] h[ ] () puig h x[] ad h[] i q. (), w g u[ ] u[ ] u[ ] for 5. (c) & u[ ] for Sic h[] u[] h[] will b o zro for So rag of is { o } y[] Giv sigal x() si / ( ) d (a) si / ( ) d x() ( /a) a hr a si / ( ) d h() u() u() si / ( ) d.(a) Giv y[] x[] * h[] x() ( a) x(a) ( a) hr a si / ( )d x() Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
18 (8) (Ts - 8)- Novmbr 7 6. (b) x() x() si / L y() x () * x () () x () u() o comparig by giv x () u( ) y() So, y() x ( ) x ( )d [from q. () [ u( ) u( )d from q. () u( ) x ( ) x ( ) & x ( ) u( ) u( ( ( )) + If + < or < h y() for So, y() () u( ) d (.) y() 7. (a) 8. (b) 9.(c) 9. Giv y[] x[] * h[] So y[] x[]h[ ] Puig h valus of x[] ad h[], w g a u[] u[ ] Sic u[] for u[ ] for So, y[] a y[] a + a + a + a Bcaus x[], h[] is valid for bcaus u[] for y[] + a + a + a y[] y[] a a a a u[] Cojuga symmric x[] (x[]) CS x[] x * [ ] x[] [ 5j + j ] x*[ ] [ j 5j] x() + x* [ ] [ 5j 5j] x[] x * [ ] [.5j j.5] If x() is ral h a mus b cojuga symmric Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
19 (Ts - 8)- Novmbr 7 (9).(c) a As a * a * a ; for all valus of j ( j) a a * ( ) Sic his is o ru i his cas so x() is o ral. If x() is v, h x() x( ) Sic his is ru for his cas, so x() is v. a +(a ) a a j j W ow X(j ) ( ) x() j j d () a By puig h valu of x(), w g X(j ) X(j ) j u( ) d ( j ) u( ) d Sic u( ) for, so. (b) W ow x() Pu j X( ) d x() X( ) d from giv figur of x() i is clar ha x() so X( ) d.56 Giv x() si x() si x() Sa( )...() si Sa() L x() A Sa()...() o comparig q () ad (), w g A A Sa() x() x( ) FT A /K X(j ) ( j ) d Puig valu of x() from q () X(j ) ( j ) ( j ) Sa () FT x( ) / X j j j. (c) Sa ( ) FT Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
20 () (Ts - 8)- Novmbr 7 x( ) h(). (c) usig Prsrval Egry horm E E E Giv x( ) d () d X(j ) ( ) ( ) ( 5) Taig ivrs Fourir rasform x() j Sigal x() has wo complx xpoials whos fudamal frqucis ar 5 rd/ sc.ad rad/sc. Ths wo complx xpoials ar o harmoically rlad. So sigal x() is o priodic. Cosidr y() x() * h() Y(j ) X(j )H(j ) h() u() u( ) h() L h () j5 h () h() h ( ) Y(j ). (a) ' Sa ( ) h () H ( j ) H(j ) j j Sa( ) si j si ( ) ( ) ( 5) Sic wh, h H(j ) If h, H(j ) Y(j ) [ ( ) ( 5)] y() j5 y() is a complx xpoial summd wih a cosa ad y() is priodic Sic w ow A Sa() A A A L si() si() si y () x () () A A A X (j ) Y (j ) Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
21 (Ts - 8)- Novmbr 7 () x () y () X (j ) * Y (j ) from q. () Usig parsval s rlaio x() d T (a ) T si L x () x (j ) si * x () X'(j ) x () from q. () dx (j ) j d si d(x( j )) j d si j/ x(j ) j/ () j / X(j ) j / ohrwis T Sic x() d (a ) x() d (giv) (a ) + (a ) a (a ) a a 6. (d) j Two possibl sigals which saisfy h giv iformaio x() j j si( ) x().5 L x () j( /) j( /) (c) Sic x() is ral ad odd Fourir sris coffici a is purly imagiary ad odd hrfor a a ad a Sic a, > oly a ad a xis / X () / / +/ x() ca b rprsd i rm of x () ad x () as Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
22 () (Ts - 8)- Novmbr 7 x() x (.5) x (.5) C j / () 7. (b) x (.5).Sa x (.5) Sa x() X( j ).5j j.5.sa Sa si si si si si si Giv x() + j j j.5j j.5 j.5 + j.5 j j j( /) j( /) Sic w ow x() j C...() j x() j C C + j C + C j + C...() o comparig q () ad q. () C + C j / j / 8. (a) 9. (c) cos / cos / Th rgy of h raisd puls is E [x()] Puig h valu of x() from giv i h qusio / / / (cos ( ) ) d / cos cos d cos() cos ( ) d O solvig h igraio ad puig h uppr ad lowr limis w s E E Giv: x() x() L a 5 x() 5 5 a a Sic w ow 5 FT X( j ) C j / () x() a a u() u( ) a a Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
23 (Ts - 8)- Novmbr 7 () Usig dualiy propry, Pu i lf sid rm ad muliply by Pu i righ sid rm w g y() u() O comparig wih giv q of y(), w g a a a FT u( )); a a ( u( ) + A B C D A + B + C + D. (c). (a) x() a a a X(j ) a 5,. a( ) 5 (.) X(j.).5 Giv y() x() * h() a ; a Taig Fourir rasform boh sid w g Y( j ) X(j ). H(j )...() Taig Fourir rasform of x(), w g X( j ) as, X(j ) ( j )...() Taig Fourir rasform of h(), w g H j as, H j j Puig h valu of H(j ) ad q () from q () ad () w g...() X( j ) i Y j j ( j ) ( j ) ( j ) (By usig parial fracio) Now aig ivrs Fourir rasform of y(), w g. (a) L g() dx() d Taig Fourir rasform of giv sigal G(j ) jx(j ) si(.) j si ( ) ( ) j si cos x( ) j j j j Taig Fourir rasform of h(), w g h(j ) a j Taig Fourir rasform of x() yilds X(j ) Sic b j y() x() * h() Taig Fourir rasform boh sid Y(j ) X(j )H(j ) Puig h valu of q. () ad () Y(j ) (a j ) b j Usig parial fracio H(j ) ad () () () X(j ) from () Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
24 () (Ts - 8)- Novmbr 7 Y(j ) A B a j b j (5) Solvig for q. () ad q. (5), w obai b purly imagiary ad odd. Thrfor, a ad a a a a. (b) A B b a Y(j ) (b a) a j b j Taig ivrs Fourir rasform y() Giv a b u() u() (b a) F.T h() H(j ) x() cos X(j ) y() h() * x() ( j ) () F.T ( ) ( ) Y(j ) X(j ) H(j ) x() ( ) x( ) ( ) () Puig h valus from q. () ad q. () Y(j ) ( ) ( ) ( j( ) ( j) ( ) ( ) ( j) ( j) j ( ) j ( ) IFT j{ ( ) ( )} si a a Fially a j a j a j So, a + a + a + a 6j j(a + a + a + a ) j( 6j) 6 5. (c) H(s) H(s) s s 7s s s I.L.T. u(); R{s} s I.L.T. u( ); R {s} s 6. (b) H() u() + u( ) W ow x(s) x() s d By puig h valu of x(), w g x(s) s u() u() d O solvig ad simplifyig, w g x(s) s s s s s To drmi ROC :.(b) Sic h Fourir sris cofficis rpa a vry N, w hav a a 5, a a 6 ad a a 7 Furhr mor, sic h sigal is ral ad odd, h Fourir sris cofficis a will u() u() ; ROC > s s ; > for which boh rms covrg is > Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
25 (Ts - 8)- Novmbr 7 (5) 7. (c) Giv x() b x() b u() + b u( )...() 8. (b) b u() LT ; b s b b u( ) LT ; b s b So, Laplac rasform of x() is X(s) Giv b ; b b s b...()...() Y(z) x (z)...() x(z) IZT x[] u[] aig z rasform of x[] x(z) z x (z) z ( z) Y(Z) ( z ) y(z) z(z ) z (z ) x(z) z z [from q ()] (By addig z ad subracig z i umaraor) z z z (z ). (c). (c) x(z) 6z + 8z x[] + x[ ] z + x[ ] z O comparig, w g x[] x[ ] 6 x[ ] 8 So x[] + x[ ] + x[ ] 5 For a fii lgh sigal, h ROC is h ir pla. Thrfor, hr ca b o pols i h fii z-pla for a fii lgh sigal. Sic h sigal is absoluly summabl, h ROC mus iclud ui circl for lf sidd sigal < z < dos o iclud ui circl, so sigal is righ sidd sigal ad sabl bcaus i iclud ui circl. Giv x[] b, < b < x[] b u[] + b u[ ] b u[] Ad b ZT b z u[ ] ZT, z b b z, 9. (c) y(z) z z ( z ) Taig ivrs z-rasform of y(z) y[] u() + u() ( + ) ( + ) Usig log divisio z b So x(z), bz b z o x(z) b z b (z b) (z b ) b z b ; Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
26 (6) (Ts - 8)- Novmbr 7. (b) b z b X(s) (s )(s ) pol locaios (s+) (s+) s, Possibl ROC () ROC > () < ROC < () ROC < Img Ral () Sigal will b lf sidd sigal, sic j axis is o icludd i ROC so sysm is o sabl W ow: L.T u() ; s L.T u() ; s L.T u( ) ; s L.T u( ) Usig parial fracio for quaio () X(s) X(s) A B s s s s o solvig A, B ad () Taig ivrs Laplac rasform for quaio (). (b) x() u( ) u( ) x() ( ) u ( ) X(z) log( + az ), z > a W ow X(z) x[]z diffriaig boh sid wr z w g dx(z) dz x[]z Muliplyig by z boh sid dx(z) z. dz dx(z) z. dz x[]z x[] From q. () ad q. () az az I.Z.T x[] Z.T ( a) u(), az Z.T a a( a) u[], az z a () () z a () Combiig im shifig propry o q. () yilds a( a) u[ ] Z.T z a x[] a( a) u[ ] a[ a] u[ ] x[] a, ( ) u[ ] x[] ( ) u() x[] az az, Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
27 (Ts - 8)- Novmbr 7 (7). (c) Z.T x[] X(z) ROC R x [] Z.T x[] X(z) ROC R/ T s 5 µ sc So samplig frqucy s will b f s T 5 s Sic m() 6 Hz cos( ) 5. (d) Z.T x [] x[] X[8z] ROC R/8 8 Sic x [] is absoluly summabl h R icluds ui circl ad X(z) has a pol z, w may coclud ha R is dfialy ousid h circl wih radius. Sic x [] is o absoluly summabl h R 8 dos o iclud h ui circl i is clar ha his is o h cas. R icluds h ui circl, R. mi R R So, R > R 8 R 8 R 8 R < 8 dos o iclud ui circl R max. So, < R < 8 wo sidd sigal as R has pol a so R mus b mor ha i.. ru for Boh sidd sigal Giv samplig im priod cos( m ) m rad / sc. [ m 6. (c) frqucy of bad limid sigal] Frqucy compos prs afr samplig f F s ± f m ( igr) wh f Hz wh f ± Hz, 8 Hz f c 5 Hz (cu off frqucy of LPF) So frqucy compo prs i h rag of 5 Hz will pass hrough LPF h (f ) LPF 8 KHz ad KHz m() m () * m () aig Fourir rasform boh sid M(j ) M (j ). M (j ) h lows frqucy compo from ( & ) will prs i m(j ) as a highs frqucy compo m() m (). m () aig fourir rasform boh sid M (j * M (j ) M(j ) h highs frqucy compo will b m() m () + m () M(j ) M (j ) + M (j ) Max (, ) will b prs as highs frqucy compo i M(j ) So x () cos() cos(,) Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
28 (8) (Ts - 8)- Novmbr 7 Nyquis ra s pla xcp {,, } rad / sc. A S X(s) x () si() si( ) X(s) d ( s ) ds ds ds s 8 rad/sc. x () si() cos() si cos ', ' rad / sc. x () si() * cos() si( ) * cos( ), 7. (b) [mi(, )] mi, 6 rad / sc. From giv fucio of x(), i ca b wri as x() u() u( ) L.T u() s L.T u( ) s s By aig Laplac rasform of x(), w g X(s) s s Sic h giv sigal is a fii duraio sigal so rgio of covrgc will b whol 8. (c) s X(s) s X(s) X(s) so (idrmia) ROC whol s pla xclud ( ) Th pols of z-rasform obaid from characrisic q z j, z j, z, z Basd o hs pol locaios, w may choos from h followig rgios of covrgc (i) z (ii) z (iii) z 9. (a) Characrisic quaio 5 z z z 8 If x() x () x () h x(j ) x (j ) * x (j ) whr * do covoluio highs frqucy compo i b. x(j ) will Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
29 (Ts - 8)- Novmbr 7 (9) 5. (c) x() Sa () Sa (8) LT For Sa () 8 LT For Sa (8) 8 So Nyquis ra ( ) [ 8 ] [ ] 6 As iiial codiio y[ ] is giv h us uilral z-rasform (U.Z.T) U.ZT y[ ] z Y(z) y[ ] So by usig giv q. (aig z rasform) z Y(z) Y[ ] + Y(z) X(z) () as zro ipu rspos x[], X(z) So, q. () bcom as Y(z) y[ ] z z (z) () Taig ivrs uilral z-rasform of q. () y[] u[] Rgd. offic : F-6, (Lowr Basm), Kawaria Sarai, Nw Dlhi-6 Pho : -656 Mobil : 89955, ifo@ismasrpublicaios.com, ifo@ismasr.org
Response of LTI Systems to Complex Exponentials
3 Fourir sris coiuous-im Rspos of LI Sysms o Complx Expoials Ouli Cosidr a LI sysm wih h ui impuls rspos Suppos h ipu sigal is a complx xpoial s x s is a complx umbr, xz zis a complx umbr h or h h w will
More informationFourier Series: main points
BIOEN 3 Lcur 6 Fourir rasforms Novmbr 9, Fourir Sris: mai pois Ifii sum of sis, cosis, or boh + a a cos( + b si( All frqucis ar igr mulipls of a fudamal frqucy, o F.S. ca rprs ay priodic fucio ha w ca
More informationPart B: Transform Methods. Professor E. Ambikairajah UNSW, Australia
Par B: rasform Mhods Profssor E. Ambikairaah UNSW, Ausralia Chapr : Fourir Rprsaio of Sigal. Fourir Sris. Fourir rasform.3 Ivrs Fourir rasform.4 Propris.4. Frqucy Shif.4. im Shif.4.3 Scalig.4.4 Diffriaio
More information1973 AP Calculus BC: Section I
97 AP Calculus BC: Scio I 9 Mius No Calculaor No: I his amiaio, l dos h aural logarihm of (ha is, logarihm o h bas ).. If f ( ) =, h f ( ) = ( ). ( ) + d = 7 6. If f( ) = +, h h s of valus for which f
More informationFrom Fourier Series towards Fourier Transform
From Fourir Sris owards Fourir rasform D D d D, d wh lim Dparm of Elcrical ad Compur Eiri D, d wh lim L s Cosidr a fucio G d W ca xprss D i rms of Gw D G Dparm of Elcrical ad Compur Eiri D G G 3 Dparm
More informationELECTROMAGNETIC COMPATIBILITY HANDBOOK 1. Chapter 12: Spectra of Periodic and Aperiodic Signals
ELECTOMAGNETIC COMPATIBILITY HANDBOOK Chapr : Spcra of Priodic ad Apriodic Sigals. Drmi whhr ach of h followig fucios ar priodic. If hy ar priodic, provid hir fudamal frqucy ad priod. a) x 4cos( 5 ) si(
More informationModeling of the CML FD noise-to-jitter conversion as an LPTV process
Modlig of h CML FD ois-o-ir covrsio as a LPV procss Marko Alksic. Rvisio hisory Vrsio Da Comms. //4 Firs vrsio mrgd wo docums. Cyclosaioary Nois ad Applicaio o CML Frqucy Dividr Jir/Phas Nois Aalysis fil
More informationECE351: Signals and Systems I. Thinh Nguyen
ECE35: Sigals ad Sysms I Thih Nguy FudamalsofSigalsadSysms x Fudamals of Sigals ad Sysms co. Fudamals of Sigals ad Sysms co. x x] Classificaio of sigals Classificaio of sigals co. x] x x] =xt s =x
More informationEEE 303: Signals and Linear Systems
33: Sigls d Lir Sysms Orhogoliy bw wo sigls L us pproim fucio f () by fucio () ovr irvl : f ( ) = c( ); h rror i pproimio is, () = f() c () h rgy of rror sigl ovr h irvl [, ] is, { }{ } = f () c () d =
More informationMathematical Preliminaries for Transforms, Subbands, and Wavelets
Mahmaical Prlimiaris for rasforms, Subbads, ad Wavls C.M. Liu Prcpual Sigal Procssig Lab Collg of Compur Scic Naioal Chiao-ug Uivrsiy hp://www.csi.cu.du.w/~cmliu/courss/comprssio/ Offic: EC538 (03)5731877
More informationReview Topics from Chapter 3&4. Fourier Series Fourier Transform Linear Time Invariant (LTI) Systems Energy-Type Signals Power-Type Signals
Rviw opics from Chapr 3&4 Fourir Sris Fourir rasform Liar im Ivaria (LI) Sysms Ergy-yp Sigals Powr-yp Sigals Fourir Sris Rprsaio for Priodic Sigals Dfiiio: L h sigal () b a priodic sigal wih priod. ()
More information( A) ( B) ( C) ( D) ( E)
d Smsr Fial Exam Worksh x 5x.( NC)If f ( ) d + 7, h 4 f ( ) d is 9x + x 5 6 ( B) ( C) 0 7 ( E) divrg +. (NC) Th ifii sris ak has h parial sum S ( ) for. k Wha is h sum of h sris a? ( B) 0 ( C) ( E) divrgs
More informationFourier Techniques Chapters 2 & 3, Part I
Fourir chiqus Chaprs & 3, Par I Dr. Yu Q. Shi Dp o Elcrical & Compur Egirig Nw Jrsy Isiu o chology Email: shi@i.du usd or h cours: , 4 h Ediio, Lahi ad Dog, Oord
More informationPoisson Arrival Process
1 Poisso Arrival Procss Arrivals occur i) i a mmorylss mar ii) [ o arrival durig Δ ] = λδ + ( Δ ) P o [ o arrival durig Δ ] = 1 λδ + ( Δ ) P o P j arrivals durig Δ = o Δ for j = 2,3, ( ) o Δ whr lim =
More informationMAT3700. Tutorial Letter 201/2/2016. Mathematics III (Engineering) Semester 2. Department of Mathematical sciences MAT3700/201/2/2016
MAT3700/0//06 Tuorial Lr 0//06 Mahmaics III (Egirig) MAT3700 Smsr Dparm of Mahmaical scics This uorial lr coais soluios ad aswrs o assigms. BARCODE CONTENTS Pag SOLUTIONS ASSIGNMENT... 3 SOLUTIONS ASSIGNMENT...
More informationPoisson Arrival Process
Poisso Arrival Procss Arrivals occur i) i a mmylss mar ii) [ o arrival durig Δ ] = λδ + ( Δ ) P o [ o arrival durig Δ ] = λδ + ( Δ ) P o P j arrivals durig Δ = o Δ f j = 2,3, o Δ whr lim =. Δ Δ C C 2 C
More information(A) 1 (B) 1 + (sin 1) (C) 1 (sin 1) (D) (sin 1) 1 (C) and g be the inverse of f. Then the value of g'(0) is. (C) a. dx (a > 0) is
[STRAIGHT OBJECTIVE TYPE] l Q. Th vlu of h dfii igrl, cos d is + (si ) (si ) (si ) Q. Th vlu of h dfii igrl si d whr [, ] cos cos Q. Vlu of h dfii igrl ( si Q. L f () = d ( ) cos 7 ( ) )d d g b h ivrs
More informationECEN620: Network Theory Broadband Circuit Design Fall 2014
ECE60: work Thory Broadbad Circui Dig Fall 04 Lcur 6: PLL Trai Bhavior Sam Palrmo Aalog & Mixd-Sigal Cr Txa A&M Uivriy Aoucm, Agda, & Rfrc HW i du oday by 5PM PLL Trackig Rpo Pha Dcor Modl PLL Hold Rag
More informationNote 6 Frequency Response
No 6 Frqucy Rpo Dparm of Mchaical Egirig, Uivriy Of Sakachwa, 57 Campu Driv, Sakaoo, S S7N 59, Caada Dparm of Mchaical Egirig, Uivriy Of Sakachwa, 57 Campu Driv, Sakaoo, S S7N 59, Caada. alyical Exprio
More informationContinous system: differential equations
/6/008 Coious sysm: diffrial quaios Drmiisic modls drivaivs isad of (+)-( r( compar ( + ) R( + r ( (0) ( R ( 0 ) ( Dcid wha hav a ffc o h sysm Drmi whhr h paramrs ar posiiv or gaiv, i.. giv growh or rducio
More informationMixing time with Coupling
Mixig im wih Couplig Jihui Li Mig Zhg Saisics Dparm May 7 Goal Iroducio o boudig h mixig im for MCMC wih couplig ad pah couplig Prsig a simpl xampl o illusra h basic ida Noaio M is a Markov chai o fii
More informationLinear Systems Analysis in the Time Domain
Liar Sysms Aalysis i h Tim Domai Firs Ordr Sysms di vl = L, vr = Ri, d di L + Ri = () d R x= i, x& = x+ ( ) L L X() s I() s = = = U() s E() s Ls+ R R L s + R u () = () =, i() = L i () = R R Firs Ordr Sysms
More informationAdvanced Engineering Mathematics, K.A. Stroud, Dexter J. Booth Engineering Mathematics, H.K. Dass Higher Engineering Mathematics, Dr. B.S.
Rfrc: (i) (ii) (iii) Advcd Egirig Mhmic, K.A. Sroud, Dxr J. Booh Egirig Mhmic, H.K. D Highr Egirig Mhmic, Dr. B.S. Grwl Th mhod of m Thi coi of h followig xm wih h giv coribuio o h ol. () Mid-rm xm : 3%
More informationNAME: SOLUTIONS EEE 203 HW 1
NAME: SOLUIONS EEE W Problm. Cosir sigal os grap is so blo. Sc folloig sigals: -, -, R, r R os rflcio opraio a os sif la opraio b. - - R - Problm. Dscrib folloig sigals i rms of lmar fcios,,r, a comp a.
More informationPractice papers A and B, produced by Edexcel in 2009, with mark schemes. Practice Paper A. 5 cosh x 2 sinh x = 11,
Prai paprs A ad B, produd by Edl i 9, wih mark shms Prai Papr A. Fid h valus of for whih 5 osh sih =, givig your aswrs as aural logarihms. (Toal 6 marks) k. A = k, whr k is a ral osa. 9 (a) Fid valus of
More informationNumerical Simulation for the 2-D Heat Equation with Derivative Boundary Conditions
IOSR Joural of Applid Chmisr IOSR-JAC -ISSN: 78-576.Volum 9 Issu 8 Vr. I Aug. 6 PP 4-8 www.iosrjourals.org Numrical Simulaio for h - Ha Equaio wih rivaiv Boudar Codiios Ima. I. Gorial parm of Mahmaics
More information3.2. Derivation of Laplace Transforms of Simple Functions
3. aplac Tarform 3. PE TRNSFORM wid rag of girig ym ar modld mahmaically by uig diffrial quaio. I gral, h diffrial quaio of h ordr ym i wri: d y( a d d d y( dy( a a y( f( (3. d Which i alo ow a a liar
More information15. Numerical Methods
S K Modal' 5. Numrical Mhod. Th quaio + 4 4 i o b olvd uig h Nwo-Rapho mhod. If i ak a h iiial approimaio of h oluio, h h approimaio uig hi mhod will b [EC: GATE-7].(a (a (b 4 Nwo-Rapho iraio chm i f(
More information15/03/1439. Lectures on Signals & systems Engineering
Lcturs o Sigals & syms Egirig Dsigd ad Prd by Dr. Ayma Elshawy Elsfy Dpt. of Syms & Computr Eg. Al-Azhar Uivrsity Email : aymalshawy@yahoo.com A sigal ca b rprd as a liar combiatio of basic sigals. Th
More informationChapter 3 Linear Equations of Higher Order (Page # 144)
Ma Modr Dirial Equaios Lcur wk 4 Jul 4-8 Dr Firozzama Darm o Mahmaics ad Saisics Arizoa Sa Uivrsi This wk s lcur will covr har ad har 4 Scios 4 har Liar Equaios o Highr Ordr Pag # 44 Scio Iroducio: Scod
More information) and furthermore all X. The definition of the term stationary requires that the distribution fulfills the condition:
Assigm Thomas Aam, Spha Brumm, Haik Lor May 6 h, 3 8 h smsr, 357, 7544, 757 oblm For R b X a raom variabl havig ormal isribuio wih ma µ a variac σ (his is wri as ~ (,) X. by: R a. Is X ) a urhrmor all
More informationWeb-appendix 1: macro to calculate the range of ( ρ, for which R is positive definite
Wb-basd Supplmary Marials for Sampl siz cosidraios for GEE aalyss of hr-lvl clusr radomizd rials by Sv Trsra, Big Lu, oh S. Prissr, Tho va Achrbrg, ad Gorg F. Borm Wb-appdix : macro o calcula h rag of
More informationEXERCISE - 01 CHECK YOUR GRASP
DEFNTE NTEGRATON EXERCSE - CHECK YOUR GRASP. ( ) d [ ] d [ ] d d ƒ( ) ƒ '( ) [ ] [ ] 8 5. ( cos )( c)d 8 ( cos )( c)d + 8 ( cos )( c) d 8 ( cos )( c) d sic + cos 8 is lwys posiiv f() d ( > ) ms f() is
More informationWhat Is the Difference between Gamma and Gaussian Distributions?
Applid Mahmaics,,, 85-89 hp://ddoiorg/6/am Publishd Oli Fbruary (hp://wwwscirporg/joural/am) Wha Is h Diffrc bw Gamma ad Gaussia Disribuios? iao-li Hu chool of Elcrical Egirig ad Compur cic, Uivrsiy of
More informationAE57/AC51/AT57 SIGNALS AND SYSTEMS DECEMBER 2012
AE7/AC/A7 SIGNALS AND SYSEMS DECEMBER Q. Drmi powr d rgy of h followig igl j i ii =A co iii = Solio: i E P I I l jw l I d jw d d Powr i fii, i i powr igl ii =A cow E P I co w d / co l I I l d wd d Powr
More informationInstitute of Actuaries of India
Insiu of Acuaris of India ubjc CT3 Probabiliy and Mahmaical aisics Novmbr Examinaions INDICATIVE OLUTION Pag of IAI CT3 Novmbr ol. a sampl man = 35 sampl sandard dviaion = 36.6 b for = uppr bound = 35+*36.6
More informationPhysics 160 Lecture 3. R. Johnson April 6, 2015
Physics 6 Lcur 3 R. Johnson April 6, 5 RC Circui (Low-Pass Filr This is h sam RC circui w lookd a arlir h im doma, bu hr w ar rsd h frquncy rspons. So w pu a s wav sad of a sp funcion. whr R C RC Complx
More informationDepartment of Electronics & Telecommunication Engineering C.V.Raman College of Engineering
Lcur No Lcur-6-9 Ar rdig his lsso, you will lr ou Fourir sris xpsio rigoomric d xpoil Propris o Fourir Sris Rspos o lir sysm Normlizd powr i Fourir xpsio Powr spcrl dsiy Ec o rsr ucio o PSD. FOURIER SERIES
More informationSolutions Manual 4.1. nonlinear. 4.2 The Fourier Series is: and the fundamental frequency is ω 2π
Soluios Maual. (a) (b) (c) (d) (e) (f) (g) liear oliear liear liear oliear oliear liear. The Fourier Series is: F () 5si( ) ad he fudameal frequecy is ω f ----- H z.3 Sice V rms V ad f 6Hz, he Fourier
More informationCSE 245: Computer Aided Circuit Simulation and Verification
CSE 45: Compur Aidd Circui Simulaion and Vrificaion Fall 4, Sp 8 Lcur : Dynamic Linar Sysm Oulin Tim Domain Analysis Sa Equaions RLC Nwork Analysis by Taylor Expansion Impuls Rspons in im domain Frquncy
More informationLecture 12: Introduction to nonlinear optics II.
Lcur : Iroduco o olar opcs II r Kužl ropagao of srog opc sgals propr olar ffcs Scod ordr ffcs! Thr-wav mxg has machg codo! Scod harmoc grao! Sum frqucy grao! aramrc grao Thrd ordr ffcs! Four-wav mxg! Opcal
More informationUNIT I FOURIER SERIES T
UNIT I FOURIER SERIES PROBLEM : Th urig mom T o h crkh o m gi i giv or ri o vu o h crk g dgr 6 9 5 8 T 5 897 785 599 66 Epd T i ri o i. Souio: L T = i + i + i +, Sic h ir d vu o T r rpd gc o T T i T i
More informationAnalysis of Non-Sinusoidal Waveforms Part 2 Laplace Transform
Aalyi o No-Siuoidal Wavorm Par Laplac raorm I h arlir cio, w lar ha h Fourir Sri may b wri i complx orm a ( ) C jω whr h Fourir coici C i giv by o o jωo C ( ) d o I h ymmrical orm, h Fourir ri i wri wih
More information1985 AP Calculus BC: Section I
985 AP Calculus BC: Sctio I 9 Miuts No Calculator Nots: () I this amiatio, l dots th atural logarithm of (that is, logarithm to th bas ). () Ulss othrwis spcifid, th domai of a fuctio f is assumd to b
More informationChapter 2 Infinite Series Page 1 of 11. Chapter 2 : Infinite Series
Chatr Ifiit Sris Pag of Sctio F Itgral Tst Chatr : Ifiit Sris By th d of this sctio you will b abl to valuat imror itgrals tst a sris for covrgc by alyig th itgral tst aly th itgral tst to rov th -sris
More informationControl Systems. Transient and Steady State Response.
Corol Sym Trai a Say Sa Ro chibum@oulch.ac.kr Ouli Tim Domai Aalyi orr ym Ui ro Ui ram ro Ui imul ro Chibum L -Soulch Corol Sym Tim Domai Aalyi Afr h mahmaical mol of h ym i obai, aalyi of ym rformac i.
More informationFOURIER ANALYSIS Signals and System Analysis
FOURIER ANALYSIS Isc Nwo Whi ligh cosiss of sv compos J Bpis Josph Fourir Bor: Mrch 768 i Auxrr, Bourgog, Frc Did: 6 My 83 i Pris, Frc Fourir Sris A priodic sigl of priod T sisfis ft f for ll f f for ll
More informationUNIT 6 Signals and Systems
UNIT 6 ONE MARK MCQ 6. dy dy The differeial equaio y x( ) d d + describes a sysem wih a ipu x () ad a oupu y. () The sysem, which is iiially relaxed, is excied by a ui sep ipu. The oupu y^h ca be represeed
More informationMicroscopic Flow Characteristics Time Headway - Distribution
CE57: Traffic Flow Thory Spring 20 Wk 2 Modling Hadway Disribuion Microscopic Flow Characrisics Tim Hadway - Disribuion Tim Hadway Dfiniion Tim Hadway vrsus Gap Ahmd Abdl-Rahim Civil Enginring Dparmn,
More informationFinal Exam : Solutions
Comp : Algorihm and Daa Srucur Final Exam : Soluion. Rcuriv Algorihm. (a) To bgin ind h mdian o {x, x,... x n }. Sinc vry numbr xcp on in h inrval [0, n] appar xacly onc in h li, w hav ha h mdian mu b
More informationSignal & Linear System Analysis
Pricipl of Commuicaio I Fall, Sigal & Liar Sym Aalyi Sigal & Liar Sym Aalyi Sigal Modl ad Claificaio Drmiiic v. Radom Drmiiic igal: complly pcifid fucio of im. Prdicabl, o ucraiy.g., < < ; whr A ad ω ar
More informationChapter4 Time Domain Analysis of Control System
Chpr4 im Domi Alyi of Corol Sym Rouh biliy cririo Sdy rror ri rpo of h fir-ordr ym ri rpo of h cod-ordr ym im domi prformc pcificio h rliohip bw h prformc pcificio d ym prmr ri rpo of highr-ordr ym Dfiiio
More informationEGR 544 Communication Theory
EGR 544 Commuicaio heory 7. Represeaio of Digially Modulaed Sigals II Z. Aliyazicioglu Elecrical ad Compuer Egieerig Deparme Cal Poly Pomoa Represeaio of Digial Modulaio wih Memory Liear Digial Modulaio
More informationChapter 2 The Poisson Process
Chapr 2 Th oisso rocss 2. Expoial ad oisso disribuios 2... Th Birh Modl I scods, a oal of popl ar bor. Sarig a ay poi i im, wha is h waiig im for h firs birh? I milliscods, a oal of lpho calls arriv a
More informationChapter 3 Fourier Series Representation of Periodic Signals
Chptr Fourir Sris Rprsttio of Priodic Sigls If ritrry sigl x(t or x[] is xprssd s lir comitio of som sic sigls th rspos of LI systm coms th sum of th idividul rsposs of thos sic sigls Such sic sigl must:
More informationz 1+ 3 z = Π n =1 z f() z = n e - z = ( 1-z) e z e n z z 1- n = ( 1-z/2) 1+ 2n z e 2n e n -1 ( 1-z )/2 e 2n-1 1-2n -1 1 () z
Sris Expasio of Rciprocal of Gamma Fuctio. Fuctios with Itgrs as Roots Fuctio f with gativ itgrs as roots ca b dscribd as follows. f() Howvr, this ifiit product divrgs. That is, such a fuctio caot xist
More informationUNIT III STANDARD DISTRIBUTIONS
UNIT III STANDARD DISTRIBUTIONS Biomial, Poisso, Normal, Gomric, Uiform, Eoial, Gamma disribuios ad hir roris. Prard by Dr. V. Valliammal Ngaiv biomial disribuios Prard by Dr.A.R.VIJAYALAKSHMI Sadard Disribuios
More informationNON-LINEAR PARAMETER ESTIMATION USING VOLTERRA SERIES WITH MULTI-TONE EXCITATION
NON-LINER PRMETER ESTIMTION USING VOLTERR SERIES WIT MULTI-TONE ECITTION imsh Char Dparm of Mchaical Egirig Visvsvaraya Rgioal Collg of Egirig Nagpur INDI-00 Naliash Vyas Dparm of Mchaical Egirig Iia Isiu
More informationTime : 1 hr. Test Paper 08 Date 04/01/15 Batch - R Marks : 120
Tim : hr. Tst Papr 8 D 4//5 Bch - R Marks : SINGLE CORRECT CHOICE TYPE [4, ]. If th compl umbr z sisfis th coditio z 3, th th last valu of z is qual to : z (A) 5/3 (B) 8/3 (C) /3 (D) o of ths 5 4. Th itgral,
More informationEE 350 Signals and Systems Spring 2005 Sample Exam #2 - Solutions
EE 35 Signals an Sysms Spring 5 Sampl Exam # - Soluions. For h following signal x( cos( sin(3 - cos(5 - T, /T x( j j 3 j 3 j j 5 j 5 j a -, a a -, a a - ½, a 3 /j-j -j/, a -3 -/jj j/, a 5 -½, a -5 -½,
More information( ) C R. υ in RC 1. cos. ,sin. ω ω υ + +
Oscillaors. Thory of Oscillaions. Th lad circui, h lag circui and h lad-lag circui. Th Win Bridg oscillaor. Ohr usful oscillaors. Th 555 Timr. Basic Dscripion. Th S flip flop. Monosabl opraion of h 555
More informationEE Control Systems LECTURE 11
Up: Moy, Ocor 5, 7 EE 434 - Corol Sy LECTUE Copyrigh FL Lwi 999 All righ rrv POLE PLACEMET A STEA-STATE EO Uig fc, o c ov h clo-loop pol o h h y prforc iprov O c lo lc uil copor o oi goo y- rcig y uyig
More informationF.Y. Diploma : Sem. II [AE/CH/FG/ME/PT/PG] Applied Mathematics
F.Y. Diploma : Sem. II [AE/CH/FG/ME/PT/PG] Applied Mahemaics Prelim Quesio Paper Soluio Q. Aemp ay FIVE of he followig : [0] Q.(a) Defie Eve ad odd fucios. [] As.: A fucio f() is said o be eve fucio if
More informationEE415/515 Fundamentals of Semiconductor Devices Fall 2012
3 EE4555 Fudmls of Smicoducor vics Fll cur 8: PN ucio iod hr 8 Forwrd & rvrs bis Moriy crrir diffusio Brrir lowrd blcd by iffusio rducd iffusio icrsd mioriy crrir drif rif hcd 3 EE 4555. E. Morris 3 3
More informationDTFT Properties. Example - Determine the DTFT Y ( e ) of n. Let. We can therefore write. From Table 3.1, the DTFT of x[n] is given by 1
DTFT Proprtis Exampl - Dtrmi th DTFT Y of y α µ, α < Lt x α µ, α < W ca thrfor writ y x x From Tabl 3., th DTFT of x is giv by ω X ω α ω Copyright, S. K. Mitra Copyright, S. K. Mitra DTFT Proprtis DTFT
More informationThe Development of Suitable and Well-founded Numerical Methods to Solve Systems of Integro- Differential Equations,
Shiraz Uivrsiy of Tchology From h SlcdWorks of Habibolla Laifizadh Th Dvlopm of Suiabl ad Wll-foudd Numrical Mhods o Solv Sysms of Igro- Diffrial Equaios, Habibolla Laifizadh, Shiraz Uivrsiy of Tchology
More information1a.- Solution: 1a.- (5 points) Plot ONLY three full periods of the square wave MUST include the principal region.
INEL495 SIGNALS AND SYSEMS FINAL EXAM: Ma 9, 8 Pro. Doigo Rodrígz SOLUIONS Probl O: Copl Epoial Forir Sri A priodi ri ar wav l ad a daal priod al o o od. i providd wi a a 5% d a.- 5 poi: Plo r ll priod
More informationChapter 6 Folding. Folding
Chaptr 6 Folding Wintr 1 Mokhtar Abolaz Folding Th folding transformation is usd to systmatically dtrmin th control circuits in DSP architctur whr multipl algorithm oprations ar tim-multiplxd to a singl
More informationPhys463.nb Conductivity. Another equivalent definition of the Fermi velocity is
39 Anohr quival dfiniion of h Fri vlociy is pf vf (6.4) If h rgy is a quadraic funcion of k H k L, hs wo dfiniions ar idical. If is NOT a quadraic funcion of k (which could happ as will b discussd in h
More information, then the old equilibrium biomass was greater than the new B e. and we want to determine how long it takes for B(t) to reach the value B e.
SURPLUS PRODUCTION (coiud) Trasiio o a Nw Equilibrium Th followig marials ar adapd from lchr (978), o h Rcommdd Radig lis caus () approachs h w quilibrium valu asympoically, i aks a ifii amou of im o acually
More informationMECE 3320 Measurements & Instrumentation. Static and Dynamic Characteristics of Signals
MECE 330 MECE 330 Masurms & Isrumao Sac ad Damc Characrscs of Sgals Dr. Isaac Chouapall Dparm of Mchacal Egrg Uvrs of Txas Pa Amrca MECE 330 Sgal Cocps A sgal s h phscal formao abou a masurd varabl bg
More information2 Dirac delta function, modeling of impulse processes. 3 Sine integral function. Exponential integral function
Chapr VII Spcial Fucios Ocobr 7, 7 479 CHAPTER VII SPECIAL FUNCTIONS Cos: Havisid sp fucio, filr fucio Dirac dla fucio, modlig of impuls procsss 3 Si igral fucio 4 Error fucio 5 Gamma fucio E Epoial igral
More informationDEPARTMENT OF ELECTRICAL &ELECTRONICS ENGINEERING SIGNALS AND SYSTEMS. Assoc. Prof. Dr. Burak Kelleci. Spring 2018
DEPARTMENT OF ELECTRICAL &ELECTRONICS ENGINEERING SIGNALS AND SYSTEMS Aoc. Prof. Dr. Burak Kllci Spring 08 OUTLINE Th Laplac Tranform Rgion of convrgnc for Laplac ranform Invr Laplac ranform Gomric valuaion
More informationChapter 3: Fourier Representation of Signals and LTI Systems. Chih-Wei Liu
Chapr 3: Fourir Rprsnaion of Signals and LTI Sysms Chih-Wi Liu Oulin Inroducion Complx Sinusoids and Frquncy Rspons Fourir Rprsnaions for Four Classs of Signals Discr-im Priodic Signals Fourir Sris Coninuous-im
More information(Reference: sections in Silberberg 5 th ed.)
ALE. Atomic Structur Nam HEM K. Marr Tam No. Sctio What is a atom? What is th structur of a atom? Th Modl th structur of a atom (Rfrc: sctios.4 -. i Silbrbrg 5 th d.) Th subatomic articls that chmists
More informationPURE MATHEMATICS A-LEVEL PAPER 1
-AL P MATH PAPER HONG KONG EXAMINATIONS AUTHORITY HONG KONG ADVANCED LEVEL EXAMINATION PURE MATHEMATICS A-LEVEL PAPER 8 am am ( hours) This papr must b aswrd i Eglish This papr cosists of Sctio A ad Sctio
More informationPI3B V, 16-Bit to 32-Bit FET Mux/DeMux NanoSwitch. Features. Description. Pin Configuration. Block Diagram.
33V, 6-Bi o 32-Bi FET Mux/DeMux NaoSwich Feaures -ohm Swich Coecio Bewee Two Pors Near-Zero Propagaio Delay Fas Swichig Speed: 4s (max) Ulra -Low Quiesce Power (02mA yp) Ideal for oebook applicaios Idusrial
More informationDiscrete Fourier Transform (DFT)
Discrt Fourir Trasorm DFT Major: All Egirig Majors Authors: Duc guy http://umricalmthods.g.us.du umrical Mthods or STEM udrgraduats 8/3/29 http://umricalmthods.g.us.du Discrt Fourir Trasorm Rcalld th xpotial
More informationOption 3. b) xe dx = and therefore the series is convergent. 12 a) Divergent b) Convergent Proof 15 For. p = 1 1so the series diverges.
Optio Chaptr Ercis. Covrgs to Covrgs to Covrgs to Divrgs Covrgs to Covrgs to Divrgs 8 Divrgs Covrgs to Covrgs to Divrgs Covrgs to Covrgs to Covrgs to Covrgs to 8 Proof Covrgs to π l 8 l a b Divrgt π Divrgt
More informationDiscrete Fourier Transform. Nuno Vasconcelos UCSD
Discrt Fourir Trasform uo Vascoclos UCSD Liar Shift Ivariat (LSI) systms o of th most importat cocpts i liar systms thory is that of a LSI systm Dfiitio: a systm T that maps [ ito y[ is LSI if ad oly if
More informationIdeal Amplifier/Attenuator. Memoryless. where k is some real constant. Integrator. System with memory
Liear Time-Ivaria Sysems (LTI Sysems) Oulie Basic Sysem Properies Memoryless ad sysems wih memory (saic or dyamic) Causal ad o-causal sysems (Causaliy) Liear ad o-liear sysems (Lieariy) Sable ad o-sable
More informationChap 2: Reliability and Availability Models
Chap : lably ad valably Modls lably = prob{s s fully fucog [,]} Suppos from [,] m prod, w masur ou of N compos, of whch N : # of compos oprag corrcly a m N f : # of compos whch hav fald a m rlably of h
More informationSection 8 Convolution and Deconvolution
APPLICATIONS IN SIGNAL PROCESSING Secio 8 Covoluio ad Decovoluio This docume illusraes several echiques for carryig ou covoluio ad decovoluio i Mahcad. There are several operaors available for hese fucios:
More informationLectures 9 IIR Systems: First Order System
EE3054 Sigals ad Systms Lcturs 9 IIR Systms: First Ordr Systm Yao Wag Polytchic Uivrsity Som slids icludd ar xtractd from lctur prstatios prpard by McCllla ad Schafr Lics Ifo for SPFirst Slids This work
More informationS.Y. B.Sc. (IT) : Sem. III. Applied Mathematics. Q.1 Attempt the following (any THREE) [15]
S.Y. B.Sc. (IT) : Sm. III Applid Mahmaics Tim : ½ Hrs.] Prlim Qusion Papr Soluion [Marks : 75 Q. Amp h following (an THREE) 3 6 Q.(a) Rduc h mari o normal form and find is rank whr A 3 3 5 3 3 3 6 Ans.:
More informationSECTION where P (cos θ, sin θ) and Q(cos θ, sin θ) are polynomials in cos θ and sin θ, provided Q is never equal to zero.
SETION 6. 57 6. Evaluation of Dfinit Intgrals Exampl 6.6 W hav usd dfinit intgrals to valuat contour intgrals. It may com as a surpris to larn that contour intgrals and rsidus can b usd to valuat crtain
More informationChapter 4 - The Fourier Series
M. J. Robrts - 8/8/4 Chaptr 4 - Th Fourir Sris Slctd Solutios (I this solutio maual, th symbol,, is usd for priodic covolutio bcaus th prfrrd symbol which appars i th txt is ot i th fot slctio of th word
More information10.3 Autocorrelation Function of Ergodic RP 10.4 Power Spectral Density of Ergodic RP 10.5 Normal RP (Gaussian RP)
ENGG450 Probabiliy ad Saisics for Egieers Iroducio 3 Probabiliy 4 Probabiliy disribuios 5 Probabiliy Desiies Orgaizaio ad descripio of daa 6 Samplig disribuios 7 Ifereces cocerig a mea 8 Comparig wo reames
More information07 - SEQUENCES AND SERIES Page 1 ( Answers at he end of all questions ) b, z = n
07 - SEQUENCES AND SERIES Pag ( Aswrs at h d of all qustios ) ( ) If = a, y = b, z = c, whr a, b, c ar i A.P. ad = 0 = 0 = 0 l a l
More informationSampling. AD Conversion (Additional Material) Sampling: Band limited signal. Sampling. Sampling function (sampling comb) III(x) Shah.
AD Coversio (Addiioal Maerial Samplig Samplig Properies of real ADCs wo Sep Flash ADC Pipelie ADC Iegraig ADCs: Sigle Slope, Dual Slope DA Coverer Samplig fucio (samplig comb III(x Shah III III ( x = δ
More informationECE594I Notes set 6: Thermal Noise
C594I ots, M. odwll, copyrightd C594I Nots st 6: Thrmal Nois Mark odwll Uivrsity of Califoria, ata Barbara rodwll@c.ucsb.du 805-893-344, 805-893-36 fax frcs ad Citatios: C594I ots, M. odwll, copyrightd
More informationOutline. Overlook. Controllability measures. Observability measures. Infinite Gramians. MOR: Balanced truncation based on infinite Gramians
Ouli Ovrlook Corollabiliy masurs Obsrvabiliy masurs Ifii Gramias MOR: alacd rucaio basd o ifii Gramias Ovrlook alacd rucaio: firs balacig h ruca. Giv a I sysm: / y u d d For covic of discussio w do h sysm
More informationP a g e 5 1 of R e p o r t P B 4 / 0 9
P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e
More informationSoftware Development Cost Model based on NHPP Gompertz Distribution
Idia Joural of Scic ad Tchology, Vol 8(12), DOI: 10.17485/ijs/2015/v8i12/68332, Ju 2015 ISSN (Pri) : 0974-6846 ISSN (Oli) : 0974-5645 Sofwar Dvlopm Cos Modl basd o NHPP Gomprz Disribuio H-Chul Kim 1* ad
More informationInverse Fourier Transform. Properties of Continuous time Fourier Transform. Review. Linearity. Reading Assignment Oppenheim Sec pp.289.
Convrgnc of ourir Trnsform Rding Assignmn Oppnhim Sc 42 pp289 Propris of Coninuous im ourir Trnsform Rviw Rviw or coninuous-im priodic signl x, j x j d Invrs ourir Trnsform 2 j j x d ourir Trnsform Linriy
More information1. Solve by the method of undetermined coefficients and by the method of variation of parameters. (4)
7 Differeial equaios Review Solve by he mehod of udeermied coefficies ad by he mehod of variaio of parameers (4) y y = si Soluio; we firs solve he homogeeous equaio (4) y y = 4 The correspodig characerisic
More informationCharging of capacitor through inductor and resistor
cur 4&: R circui harging of capacior hrough inducor and rsisor us considr a capacior of capacianc is conncd o a D sourc of.m.f. E hrough a rsisr of rsisanc R, an inducor of inducanc and a y K in sris.
More informationRing of Large Number Mutually Coupled Oscillators Periodic Solutions
Iraioal Joural of horical ad Mahmaical Physics 4, 4(6: 5-9 DOI: 59/jijmp446 Rig of arg Numbr Muually Coupld Oscillaors Priodic Soluios Vasil G Aglov,*, Dafika z Aglova Dparm Nam of Mahmaics, Uivrsiy of
More informationOptimum Demodulation. Lecture Notes 9: Intersymbol Interference
d d Lcur os 9: Irsybol Irrc I his lcur w xai opiu dodulaio wh h rasid sigal is ilrd by h chal ad hr is addiiv whi Gaussia ois. h opiu dodulaor chooss h possibl rasid vcor ha would rsul i h rcivd vcor (i
More informationProblem Value Score Earned No/Wrong Rec -3 Total
GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL & COMPUTER ENGINEERING ECE6 Fall Quiz # Writt Eam Novmr, NAME: Solutio Kys GT Usram: LAST FIRST.g., gtiit Rcitatio Sctio: Circl t dat & tim w your Rcitatio
More information