Communication Systems Lecture 25. Dong In Kim School of Info/Comm Engineering Sungkyunkwan University
|
|
- Egbert James
- 6 years ago
- Views:
Transcription
1 Commuiaio Sysems Leure 5 Dog I Kim Shool o Io/Comm Egieerig Sugkyukwa Uiversiy 1
2 Oulie Noise i Agle Modulaio Phase deviaio Large SNR Small SNR Oupu SNR PM FM
3 Review o Agle Modulaio Geeral orm o agle modulaed sigal: PM: ( = os é w + ( x A ë x( = Aos éw+ kpm( ù ë û ( ( m : ormalized message wih max m = 1. é ù FM: x ( = Aos w+ p ò d m ( a d a êë úû 1 P= A. Trasmied Power: Demodulaio oupu: PM: T 1 d yd( = KD(, FM: yd( = KD p d ù û ( 3
4 Noise i Agle Modulaio ( x + Noise w(: AWGN N 0 / Predeeio Filer 1( ( e Demodulaio Badwidh o he predeeio iler: Carso s rule: B T = (D+1W. ( = éw + ( From x Aos ù ë û, To aalyze he ee o he oise, we eed o wrie ( ( e1 ( = R(os éw q e ù ë û, where e ( is he oise added o (. Posdeeio Filer Rd Redue oise (explaied laer 4
5 Noise i Agle Modulaio Predeeio iler oupu: ( = os é w + q + ( ù + ( os ( w + q - ( si ( w + q e1 Aos ë û ( os s( si = A os é w q ( ù ë + + û + r( os( w+ q+ ( os éw q ( ù ( os( w q ( ( ( = A ë + + û + r ( ( ( ( ( w + q+ ( si( ( ( ( ù ( = A os é ë w+ q+ û + r( os w+ q+ os - - r (si + + si( - ( ( ( ( A r(os oséw q ( = + - ë r (si ( w + q+ ( si( ( -( ù û 5
6 Noise i Agle Modulaio ( ( ( ( éw q ( e1 ( = A + r (os - os ë + + e ( ( w + q+ ( si ( ( ( - r (si ( ( = R(os é ë w+ q+ + e = a ù û ( ( ( ( ( r (si 1 A + r (os ( Phase deviaio rom he arrier: ( ( y( = + e Oly yphase deviaio aes he demodulaio. Ampliude a be kep osa by a limier (pp ù û
7 Agle Modulaio wih High SNR High SNR: A r( mos o he ime. r (si ( ( (si ( ( - r - -1 ( -1 ( e ( = a» a A+ r(os ( ( -( A r (si ( ( - ( r (si ( ( - ( (si -1 (si(» si» A A r ( y( = + e» + si - A A ( ( ( ( ( ( Sill domiaed by he sigal ( ireases, he ee o r ( redues! 7
8 Agle Modulaio wih Low SNR Low SNR: A r ( mos o he ime. y (: domiaed by (. y ( = ( -a (. a ( Need expressio o a ( i erms o ( ad (. Noe: e ( is wrog i Fig e 8
9 Agle Modulaio wih Low SNR Low SNR: y ( = ( -a (. a( very small i A r (. a ( a(» si a(» a a(» A y(» ( si q( r ( A - si ( ( r ( - ( 9
10 Agle Modulaio wih Low SNR Low SNR: A» - ( - y ( ( si ( ( r ( Message sigal is los a low SNR! Threshold ee. 10
11 Agle Modulaio Phase deviaio e ( (os 1 = R é ë w+ q+ y ù û ( High SNR: r ( y (» ( + si ( ( - ( (1 ( Low SNR: A Small mos o he ime A y(» ( - si ( ( - ( ( r ( Noe: Eq ( a be obaied rom (1 by swihig ( «(, ad A «r (. 11
12 Oulie Noise i Agle Modulaio Phase deviaio Large SNR Small SNR Oupu SNR PM FM 1
13 PM Oupu SNR ( = éw + q+ ( ù+ ( ( w + q - ( i ( w + q e1 Aos ë û (os s(si ( ( (os ( = R(os éw q ù R éw q ù ë e û ( ë + + y û r ( y (» + si - A PM Demodulaio oupu: ( High SNR: ( ( ( ( = y( = ( + ( y K K K D D D D e r ( = KD ( + KD si ( - ( A ( = K k m + ( D p P ( P ( 13
14 PM Oupu SNR PM Demodulaio oupu: r yd ( = KD kp m ( + KD si ( - ( A ( si ( Demod Sigal power: S = P ( K k P DP D p m To ompue oise power: le ( = 0 (message is 0 r( s( P( = KD si( = KD A A r ( ( ( s 14
15 PM Oupu SNR Reall: NBNoise N 0 / S ( S (- +B/ S (+ ( = Lp é ( - + ( + B/ S S s S ù ë û S s ( N 0 B/ 15
16 PM Oupu SNR PM Demodulaio oupu: s ( P ( KD A D = S ( = N P 0 A Sperum o s ( is i [-1/ B T, 1/ B T ] ( = ( + ( y K k m D D p P B T : Badwidh o predeeio iler (by Carso s rule. Oupu oise power: N DP = K D 0 A K N B T 16
17 PM Oupu SNR Pos-deeio i iler: Sie B T = (D+1W > W, he oupu oise power a be redued by applyig a pos-deeio iler wih badwidh W Predeeio Filer e1( Demodulaio Posdeeio Filer N DP = K D A N B 0 T N DP = K D A N W 0 17
18 PM Oupu SNR Trasmied power Per ui message badwidh 1 P= A. Trasmied Power: Oupu oise power: T D ç T 0 D A è 0 A PT = N W N W K æ P ö N = DP N W = K. ç N W ø Ireasig rasmied power redues oupu oise power! Diere rom liear modulaio. PM Demod Oupu SNR: K k P SNR = = k P DP K P N W - NW ( SNR D D p m P T k ppm T / ( 0 0 ( 1 18
19 PM Oupu SNR PM: x A é ë kpm ( = os w + ( PM Demod Oupu SNR: Sigle-oe Modulaio ( = k siw bsiw p m m ù û P SNR = k P DP NW ( SNR m ( = si w or osw m m T p m 0 b k p : Modulaio Idex SNR PT = b P m : ireasig b ireases oupu SNR. DP NW ( 0 ( b + Bb Bu badwidh B = + 1 W is also ireased. T Ipu oise power will be ireased. Eveually large ipu SNR assumpio is ivalid hreshold ee. 19
20 Oulie Noise i Agle Modulaio Phase deviaio Large SNR Small SNR Oupu SNR PM FM 0
21 FM Oupu SNR ( = A éw + q + ( ù + ( ( w + q - ( i ( w + q e1 Aos ë û (os s(si ( ( (os ( r ( y(» ( + si( ( ( - A = R(os éw + q+ + ù R éw + q+ y ù ë e û ë û High SNR: FM Demodulaio oupu: y D ( ( A K d y D = p d K d ( ì ü D KD d r ( = + í ï si ( ( ( - ý ï p d p d ï A î ïþ ( = K m + ( D d F F ( 1
22 FM Oupu SNR FM Demodulaio oupu: K ( D d ì r ü y ( ( ï si ( ( ( ï D = KD dm + í p d A - ý ï î ïþ Demod Sigal power: S F ( DF = KD d Pm To ompue oise power: le ( = 0 (message is 0 ( K ì ü (si D d r KD ds ( F ( = ï í ï ý= p d ïî A ïþ pa d (: quadraure ompoe o oise. s How o id oise psd? r ( ( ( s
23 FM Oupu SNR ( K (si D d ì r ü KD ds ( F ( = ï í ï ý= p d ï î A ï þ pa d dx( j p X ( d ( s «d/d is a liear iler d d u ( S ( = H( S ( KD KD 1 1 NF = ç ( p 0 0 T T pa = Îê- A æ ö é ù S ( N N, B, B. èç ø ê ë ú û u s 3
24 FM Oupu SNR K é 1 1 ù D SNF ( = N 0, Î - BT, BT. A ê ë úû The oise has less ee o low-req message sigals. Aer Pos-deeio iler wih badwidh W: K K NDF = N ò d = N W A W D D W 3A ò 4
25 FM Oupu SNR 1 P= A. Trasmied Power: Oupu oise power: N DF T K K W æ P ö = 3A = 3 ç N W ø D 3 D T N 0W ç è 0 A PT = N W N W Noise power is iversely proporioal p o FM Demod Oupu SNR: ( SNR DF K D d P æ m ö 3 d PT P -1 m æ P ö èç W ø D T 0 = = K W 3 ç èn W ø 0 N W P T NW 0 5
26 FM Oupu SNR FM Demod Oupu SNR: ( SNR DF æ ö = ç P N W d T 3 Pm ç èw ø 0 Reall: Deviaio Raio or geeral m(: peak requey deviaio max '( D = = badwidh o m( W é ù FM: x ( = Aos w+ p ò d m ( a d a êë úû d max m( D = d SNR W = ( DF W P SNR = D P NW T 3D Pm 0 6
27 FM Oupu SNR FM Demod Oupu SNR: P SNR = D P DF NW ( SNR T 3D Pm 0 For D 1, B =(D+1W» DW: T ( SNR DF 3æB ö T PT Pm 4 ç çèw ø 0 = N W Ireasig badwidh a improve he oupu SNR. Ipu oise power will be ireased. Eveually large ipu SNR assumpio is ivalid hreshold ee. 7
28 Pre-emphasis ad De-emphasis or Noise Pre emphasis Mod + Pre deeio Demod Pos deeio Deemphasis Demod oupu: Noise K ì ü D d r ( y ( ( si ( ( ( D = KD dm + í ï - ý ï p d ï A î ïþ Umodulaed arrier: F dx ( «d F ( ( 0 (message is 0 = ( K ì ü (si D d r KD ds ( ( = í ï ý ï= p d ïî A ïþ pa d K é 1 1 ù D j p X ( SNF ( = N 0, Î - BT, BT. A ê ë úû 8
29 Pre-emphasis ad De-emphasis or Noise Pre emphasis Mod + Pre deeio Demod Pos deeio Deemphasis Noise K 1 1 D é ù SNF ( = N0, - B,. T BT A Îê ê ë úû Assume de-emphasis iler is a 1 s -order lowpass RC iler: 1 HDE ( = 1 + ( / 3 W Noise power aer de-emphasis iler: W DF DE NF W N = ò H ( S ( d - 3 ò 9
30 ò 1 1 u du = a -1 a + u a a Pre-emphasis ad De-emphasis or Noise Pre emphasis Mod + Pre deeio Demod Pos deeio Deemphasis Noise Noise power aer de-emphasis emphasis iler: W NDF = ò HDE ( SNF ( d - W K K = N d = N d A A W W D ò D ò W W ( / K æw Wö K æw pö K = N - a» N -» N W A A A D 3-1 D 3 D ç è 3 3ø ç è 3 ø 30
31 Pre-emphasis ad De-emphasis or Noise A PT = N W N W 0 0 Pre emphasis Mod + Pre deeio Demod Pos deeio Deemphasis Noise ( = ( + ( y K m D D d F Demod Sigal power: Noise power aer de-emphasis: Oupu SNR: ( ( / P = Oupu SNR: SNR wihou deemphasis: S N DF = KD d Pm DF» SNR P T DF d 3 m NW 0 SNR PT = 3 d / W P DF m NW ( ( 0 K D A N W
32 Pre-emphasis ad De-emphasis or Noise Pre emphasis Mod + Pre deeio Demod Pos deeio Deemphasis Noise Oupu SNR wih de-emphasis: emphasis: ( = ( / SNR P T DF _ DE d 3 m NW 0 Oupu SNR wihou de-emphasis: 3 W ( = 3 ( / P PT SNR 3 d / W P DF m NW SNR a be improved sigiialy by de-emphasis iler. 0 3
33 Pre-emphasis ad De-emphasis or Noise SNR wih de-emphasis: SNR wihou de-emphasis: ( ( / P = SNR P T DF _ DE d 3 m NW 0 ( = 3 ( / P SNR W P T DF d m NW Example: FM: = 75 khz, W=15kHz, D = 5. ( SNR ( d =.1 khz, P = m PT PT SNR = 375/ = DF NW 0 NW 0 PT PT SNR = 75/ = 18 DF_ DE NW NW ( ( 0 0 Trasmied power a be redued by 17 imes, wih he same oise perormae. 0 33
Communications II Lecture 4: Effects of Noise on AM. Professor Kin K. Leung EEE and Computing Departments Imperial College London Copyright reserved
Commuiaio II Leure 4: Effe of Noie o M Profeor Ki K. Leug EEE ad Compuig Deparme Imperial College Lodo Copyrigh reerved Noie i alog Commuiaio Syem How do variou aalog modulaio heme perform i he preee of
More informationPrinciples of Communications Lecture 12: Noise in Modulation Systems. Chih-Wei Liu 劉志尉 National Chiao Tung University
Priiples of Commuiatios Leture 1: Noise i Modulatio Systems Chih-Wei Liu 劉志尉 Natioal Chiao ug Uiversity wliu@twis.ee.tu.edu.tw Outlies Sigal-to-Noise Ratio Noise ad Phase Errors i Coheret Systems Noise
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 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 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 information! " # $! % & '! , ) ( + - (. ) ( ) * + / 0 1 2 3 0 / 4 5 / 6 0 ; 8 7 < = 7 > 8 7 8 9 : Œ Š ž P P h ˆ Š ˆ Œ ˆ Š ˆ Ž Ž Ý Ü Ý Ü Ý Ž Ý ê ç è ± ¹ ¼ ¹ ä ± ¹ w ç ¹ è ¼ è Œ ¹ ± ¹ è ¹ è ä ç w ¹ ã ¼ ¹ ä ¹ ¼ ¹ ±
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 informationF O R SOCI AL WORK RESE ARCH
7 TH EUROPE AN CONFERENCE F O R SOCI AL WORK RESE ARCH C h a l l e n g e s i n s o c i a l w o r k r e s e a r c h c o n f l i c t s, b a r r i e r s a n d p o s s i b i l i t i e s i n r e l a t i o n
More informationECE-314 Fall 2012 Review Questions
ECE-34 Fall 0 Review Quesios. A liear ime-ivaria sysem has he ipu-oupu characerisics show i he firs row of he diagram below. Deermie he oupu for he ipu show o he secod row of he diagram. Jusify your aswer.
More informationWhat is a Communications System?
Wha is a ommuiaios Sysem? Aual Real Life Messae Real Life Messae Replia Ipu Sial Oupu Sial Ipu rasduer Oupu rasduer Eleroi Sial rasmier rasmied Sial hael Reeived Sial Reeiver Eleroi Sial Noise ad Disorio
More informationName:... Batch:... TOPIC: II (C) 1 sec 3 2x - 3 sec 2x. 6 é ë. logtan x (A) log (tan x) (B) cot (log x) (C) log log (tan x) (D) tan (log x) cos x (C)
Nm:... Bch:... TOPIC: II. ( + ) d cos ( ) co( ) n( ) ( ) n (D) non of hs. n sc d sc + sc é ësc sc ù û sc sc é ë ù û (D) non of hs. sc cosc d logn log (n ) co (log ) log log (n ) (D) n (log ). cos log(
More informationMATH 6101 Fall 2008 Newton and Differential Equations
MATH 611 Fall 8 Newto ad Differetial Equatios A Differetial Equatio What is a differetial equatio? A differetial equatio is a equatio relatig the quatities x, y ad y' ad possibly higher derivatives of
More informationETIKA V PROFESII PSYCHOLÓGA
P r a ž s k á v y s o k á š k o l a p s y c h o s o c i á l n í c h s t u d i í ETIKA V PROFESII PSYCHOLÓGA N a t á l i a S l o b o d n í k o v á v e d ú c i p r á c e : P h D r. M a r t i n S t r o u
More informationB Signals and Systems I Solutions to Midterm Test 2. xt ()
34-33B Signals and Sysems I Soluions o Miderm es 34-33B Signals and Sysems I Soluions o Miderm es ednesday Marh 7, 7:PM-9:PM Examiner: Prof. Benoi Boule Deparmen of Elerial and Compuer Engineering MGill
More informationFourier transform. Continuous-time Fourier transform (CTFT) ω ω
Fourier rasform Coiuous-ime Fourier rasform (CTFT P. Deoe ( he Fourier rasform of he sigal x(. Deermie he followig values, wihou compuig (. a (0 b ( d c ( si d ( d d e iverse Fourier rasform for Re { (
More informationChair Susan Pilkington called the meeting to order.
PGE PRK D RECREO DVOR COMMEE REGUR MEEG MUE MOD, JU, Ru M h P P d R d Cmm hd : m Ju,, h Cu Chmb C H P, z Ch u P dd, Mmb B C, Gm Cu D W Bd mmb b: m D, d Md z ud mmb : C M, J C P Cmmu Dm D, Km Jh Pub W M,
More informationPulse Shaping and ISI (Proakis: chapter 10.1, 10.3) EEE3012 Spring 2018
Pulse Shaping and ISI (Proakis: chapter 10.1, 10.3) EEE3012 Spring 2018 Digital Communication System Introduction Bandlimited channels distort signals the result is smeared pulses intersymol interference
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 informationLinear Time Invariant Systems
1 Liear Time Ivaria Sysems Oulie We will show ha he oupu equals he covoluio bewee he ipu ad he ui impulse respose: sysem for a discree-ime, for a coiuous-ime sysdem, y x h y x h 2 Discree Time LTI Sysems
More informationTELEMATICS LINK LEADS
EEAICS I EADS UI CD PHOE VOICE AV PREIU I EADS REQ E E A + A + I A + I E B + E + I B + E + I B + E + H B + I D + UI CD PHOE VOICE AV PREIU I EADS REQ D + D + D + I C + C + C + C + I G G + I G + I G + H
More informationBlock Diagram of a DCS in 411
Informaion source Forma A/D From oher sources Pulse modu. Muliplex Bandpass modu. X M h: channel impulse response m i g i s i Digial inpu Digial oupu iming and synchronizaion Digial baseband/ bandpass
More informationEELE Lecture 8 Example of Fourier Series for a Triangle from the Fourier Transform. Homework password is: 14445
EELE445-4 Lecure 8 Eample o Fourier Series or a riangle rom he Fourier ransorm Homework password is: 4445 3 4 EELE445-4 Lecure 8 LI Sysems and Filers 5 LI Sysem 6 3 Linear ime-invarian Sysem Deiniion o
More informationELG3175 Introduction to Communication Systems. Angle Modulation Continued
ELG3175 Iroduio o Couiaio Sye gle Modulaio Coiued Le araériique de igaux odulé e agle PM Sigal M Sigal Iaaeou phae i Iaaeou requey Maxiu phae deviaio D ax Maxiu requey deviaio D ax Power p p p x où 0 d
More informationAn Example file... log.txt
# ' ' Start of fie & %$ " 1 - : 5? ;., B - ( * * B - ( * * F I / 0. )- +, * ( ) 8 8 7 /. 6 )- +, 5 5 3 2( 7 7 +, 6 6 9( 3 5( ) 7-0 +, => - +< ( ) )- +, 7 / +, 5 9 (. 6 )- 0 * D>. C )- +, (A :, C 0 )- +,
More information6.003 Homework #5 Solutions
6. Homework #5 Soluios Problems. DT covoluio Le y represe he DT sigal ha resuls whe f is covolved wih g, i.e., y[] = (f g)[] which is someimes wrie as y[] = f[] g[]. Deermie closed-form expressios for
More informationT h e C S E T I P r o j e c t
T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T
More informationECE 350 Matlab-Based Project #3
ECE 350 Malab-Based Projec #3 Due Dae: Nov. 26, 2008 Read he aached Malab uorial ad read he help files abou fucio i, subs, sem, bar, sum, aa2. he wrie a sigle Malab M file o complee he followig ask for
More informationP a g e 3 6 of R e p o r t P B 4 / 0 9
P a g e 3 6 of R e p o r t P B 4 / 0 9 p r o t e c t h um a n h e a l t h a n d p r o p e r t y fr om t h e d a n g e rs i n h e r e n t i n m i n i n g o p e r a t i o n s s u c h a s a q u a r r y. J
More informationDavid Randall. ( )e ikx. k = u x,t. u( x,t)e ikx dx L. x L /2. Recall that the proof of (1) and (2) involves use of the orthogonality condition.
! Revised April 21, 2010 1:27 P! 1 Fourier Series David Radall Assume ha u( x,) is real ad iegrable If he domai is periodic, wih period L, we ca express u( x,) exacly by a Fourier series expasio: ( ) =
More informationHough search for continuous gravitational waves using LIGO S4 data
Hough search for coiuous graviaioal waves usig LIGO S4 daa A.M. Sies for he LIGO Scieific Collaboraio Uiversia de les Illes Balears, Spai Alber Eisei Isiu, Germay MG11, GW4- GW daa Aalysis Berli - July
More informationC(p, ) 13 N. Nuclear reactions generate energy create new isotopes and elements. Notation for stellar rates: p 12
Iroducio o sellar reacio raes Nuclear reacios geerae eergy creae ew isoopes ad elemes Noaio for sellar raes: p C 3 N C(p,) 3 N The heavier arge ucleus (Lab: arge) he ligher icomig projecile (Lab: beam)
More informationOverview in Images. 5 nm
Overview in Images 5 nm K.S. Min et al. PhD Thesis K.V. Vahala et al, Phys. Rev. Lett, 85, p.74 (000) J. D. Joannopoulos, et al, Nature, vol.386, p.143-9 (1997) S. Lin et al, Nature, vol. 394, p. 51-3,
More informationElectrical Engineering Department Network Lab.
Par:- Elecrical Egieerig Deparme Nework Lab. Deermiaio of differe parameers of -por eworks ad verificaio of heir ierrelaio ships. Objecive: - To deermie Y, ad ABD parameers of sigle ad cascaded wo Por
More information1 Notes on Little s Law (l = λw)
Copyrigh c 26 by Karl Sigma Noes o Lile s Law (l λw) We cosider here a famous ad very useful law i queueig heory called Lile s Law, also kow as l λw, which assers ha he ime average umber of cusomers i
More informationECE-305: Fall 2017 MOS Capacitors and Transistors
ECE-305: Fall 2017 MOS Capacitors and Transistors Pierret, Semiconductor Device Fundamentals (SDF) Chapters 15+16 (pp. 525-530, 563-599) Professor Peter Bermel Electrical and Computer Engineering Purdue
More informationChapter 4: Angle Modulation
57 Chapter 4: Agle Modulatio 4.1 Itrodutio to Agle Modulatio This hapter desribes frequey odulatio (FM) ad phase odulatio (PM), whih are both fors of agle odulatio. Agle odulatio has several advatages
More information. ffflffluary 7, 1855.
x B B - Y 8 B > ) - ( vv B ( v v v (B/ x< / Y 8 8 > [ x v 6 ) > ( - ) - x ( < v x { > v v q < 8 - - - 4 B ( v - / v x [ - - B v B --------- v v ( v < v v v q B v B B v?8 Y X $ v x B ( B B B B ) ( - v -
More informationBig O Notation for Time Complexity of Algorithms
BRONX COMMUNITY COLLEGE of he Ciy Uiversiy of New York DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE CSI 33 Secio E01 Hadou 1 Fall 2014 Sepember 3, 2014 Big O Noaio for Time Complexiy of Algorihms Time
More informationQ Scheme Marks AOs. Notes. Ignore any extra columns with 0 probability. Otherwise 1 for each. If 4, 5 or 6 missing B0B0.
1a k(16 9) + k(25 9) + k(36 9) (or 7k + 16k + 27k). M1 2.1 4th = 1 M1 Þ k = 1 50 (answer given). * Model simple random variables as probability (3) 1b x 4 5 6 P(X = x) 7 50 16 50 27 50 Note: decimal values
More informationKing Fahd University of Petroleum & Minerals Computer Engineering g Dept
Kig Fahd Uiversiy of Peroleum & Mierals Compuer Egieerig g Dep COE 4 Daa ad Compuer Commuicaios erm Dr. shraf S. Hasa Mahmoud Rm -4 Ex. 74 Email: ashraf@kfupm.edu.sa 9/8/ Dr. shraf S. Hasa Mahmoud Lecure
More informationLinear System Theory
Naioal Tsig Hua Uiversiy Dearme of Power Mechaical Egieerig Mid-Term Eamiaio 3 November 11.5 Hours Liear Sysem Theory (Secio B o Secio E) [11PME 51] This aer coais eigh quesios You may aswer he quesios
More informationDiscrete-Time Signals and Systems. Introduction to Digital Signal Processing. Independent Variable. What is a Signal? What is a System?
Discree-Time Sigals ad Sysems Iroducio o Digial Sigal Processig Professor Deepa Kudur Uiversiy of Toroo Referece: Secios. -.4 of Joh G. Proakis ad Dimiris G. Maolakis, Digial Sigal Processig: Priciples,
More informationDifferentiating Functions & Expressions - Edexcel Past Exam Questions
- Edecel Past Eam Questions. (a) Differentiate with respect to (i) sin + sec, (ii) { + ln ()}. 5-0 + 9 Given that y =, ¹, ( -) 8 (b) show that = ( -). (6) June 05 Q. f() = e ln, > 0. (a) Differentiate
More information6/10/2014. Definition. Time series Data. Time series Graph. Components of time series. Time series Seasonal. Time series Trend
6//4 Defiiio Time series Daa A ime series Measures he same pheomeo a equal iervals of ime Time series Graph Compoes of ime series 5 5 5-5 7 Q 7 Q 7 Q 3 7 Q 4 8 Q 8 Q 8 Q 3 8 Q 4 9 Q 9 Q 9 Q 3 9 Q 4 Q Q
More information3.4 Design Methods for Fractional Delay Allpass Filters
Chater 3. Fractional Delay Filters 15 3.4 Design Methods for Fractional Delay Allass Filters Above we have studied the design of FIR filters for fractional delay aroximation. ow we show how recursive or
More informationFramework for functional tree simulation applied to 'golden delicious' apple trees
Purdue University Purdue e-pubs Open Access Theses Theses and Dissertations Spring 2015 Framework for functional tree simulation applied to 'golden delicious' apple trees Marek Fiser Purdue University
More informationContinuous-time Fourier Methods
ELEC 321-001 SIGNALS and SYSTEMS Continuous-time Fourier Methods Chapter 6 1 Representing a Signal The convolution method for finding the response of a system to an excitation takes advantage of the linearity
More informationMin-Guk Seo, Dong-Min Park, Jae-Hoon Lee, Kyong-Hwan Kim, Yonghwan Kim
International Research Exchange Meeting of Ship and Ocean Engineering in Osaka, December 1-, Osaka, Japan Comparative Study on Added Resistance Computation Min-Guk Seo, Dong-Min Park, Jae-Hoon Lee, Kyong-Hwan
More informationSampling Example. ( ) δ ( f 1) (1/2)cos(12πt), T 0 = 1
Samplig Example Le x = cos( 4π)cos( π). The fudameal frequecy of cos 4π fudameal frequecy of cos π is Hz. The ( f ) = ( / ) δ ( f 7) + δ ( f + 7) / δ ( f ) + δ ( f + ). ( f ) = ( / 4) δ ( f 8) + δ ( f
More informationReciprocal Mixing: The trouble with oscillators
Reciprocal Mixing: The trouble with oscillators Tradeoffs in RX Noise Figure(Sensitivity) Distortion (Linearity) Phase Noise (Aliasing) James Buckwalter Phase Noise Phase noise is the frequency domain
More informationh : sh +i F J a n W i m +i F D eh, 1 ; 5 i A cl m i n i sh» si N «q a : 1? ek ser P t r \. e a & im a n alaa p ( M Scanned by CamScanner
m m i s t r * j i ega>x I Bi 5 n ì r s w «s m I L nk r n A F o n n l 5 o 5 i n l D eh 1 ; 5 i A cl m i n i sh» si N «q a : 1? { D v i H R o s c q \ l o o m ( t 9 8 6) im a n alaa p ( M n h k Em l A ma
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 informationAQA Maths M2. Topic Questions from Papers. Differential Equations. Answers
AQA Mahs M Topic Quesions from Papers Differenial Equaions Answers PhysicsAndMahsTuor.com Q Soluion Marks Toal Commens M 600 0 = A Applying Newonís second law wih 0 and. Correc equaion = 0 dm Separaing
More informationMath 2414 Homework Set 7 Solutions 10 Points
Mah Homework Se 7 Soluios 0 Pois #. ( ps) Firs verify ha we ca use he iegral es. The erms are clearly posiive (he epoeial is always posiive ad + is posiive if >, which i is i his case). For decreasig we
More informationSolutions to selected problems from the midterm exam Math 222 Winter 2015
Soluios o seleced problems from he miderm eam Mah Wier 5. Derive he Maclauri series for he followig fucios. (cf. Pracice Problem 4 log( + (a L( d. Soluio: We have he Maclauri series log( + + 3 3 4 4 +...,
More informationSUMMATION OF INFINITE SERIES REVISITED
SUMMATION OF INFINITE SERIES REVISITED I several aricles over he las decade o his web page we have show how o sum cerai iiie series icludig he geomeric series. We wa here o eed his discussio o he geeral
More informationMATH 174: Numerical Analysis I. Math Division, IMSP, UPLB 1 st Sem AY
MATH 74: Numerical Analysis I Math Division, IMSP, UPLB st Sem AY 0809 Eample : Prepare a table or the unction e or in [0,]. The dierence between adjacent abscissas is h step size. What should be the step
More informationDigital Signal Processing. Homework 2 Solution. Due Monday 4 October Following the method on page 38, the difference equation
Digital Sigal Proessig Homework Solutio Due Moda 4 Otober 00. Problem.4 Followig the method o page, the differee equatio [] (/4[-] + (/[-] x[-] has oeffiiets a0, a -/4, a /, ad b. For these oeffiiets A(z
More information= 1 3. r in. dr in. 6 dt = 1 2 A in. dt = 3 ds
. B. Consider the octagon slit u into eight isosceles triangles with vertex angle o and base angles o /. We want to calculate the aothem using the tangent half-angle formula and a right triangle with base
More informationECE-305: Fall 2017 Metal Oxide Semiconductor Devices
C-305: Fall 2017 Metal Oxide Semiconductor Devices Pierret, Semiconductor Device Fundamentals (SDF) Chapters 15+16 (pp. 525-530, 563-599) Professor Peter Bermel lectrical and Computer ngineering Purdue
More informationONE RANDOM VARIABLE F ( ) [ ] x P X x x x 3
The Cumulive Disribuio Fucio (cd) ONE RANDOM VARIABLE cd is deied s he probbiliy o he eve { x}: F ( ) [ ] x P x x - Applies o discree s well s coiuous RV. Exmple: hree osses o coi x 8 3 x 8 8 F 3 3 7 x
More informationByung-Soo Choi.
Grover Search and its Applications Bung-Soo Choi bschoi3@gmail.com Contents Basics of Quantum Computation General Properties of Grover Search Idea Analsis Weight Decision Smmetric To Weights Asmmetric
More informationNotes 03 largely plagiarized by %khc
1 1 Discree-Time Covoluio Noes 03 largely plagiarized by %khc Le s begi our discussio of covoluio i discree-ime, sice life is somewha easier i ha domai. We sar wih a sigal x[] ha will be he ipu io our
More informationDigital Modulation Schemes
Digial Modulaio cheme Digial ramiio chai igal repreeaio ime domai Frequecy domai igal pace Liear modulaio cheme Ampliude hi Keyig (AK) Phae hi Keyig (PK) Combiaio (APK, QAM) Pule hapig Coiuou Phae Modulaio
More informationProblems and Solutions for Section 3.2 (3.15 through 3.25)
3-7 Problems ad Soluios for Secio 3 35 hrough 35 35 Calculae he respose of a overdamped sigle-degree-of-freedom sysem o a arbirary o-periodic exciaio Soluio: From Equaio 3: x = # F! h "! d! For a overdamped
More informationIE 400 Principles of Engineering Management. Graphical Solution of 2-variable LP Problems
IE 400 Principles of Engineering Management Graphical Solution of 2-variable LP Problems Graphical Solution of 2-variable LP Problems Ex 1.a) max x 1 + 3 x 2 s.t. x 1 + x 2 6 - x 1 + 2x 2 8 x 1, x 2 0,
More informationFresnel Dragging Explained
Fresel Draggig Explaied 07/05/008 Decla Traill Decla@espace.e.au The Fresel Draggig Coefficie required o explai he resul of he Fizeau experime ca be easily explaied by usig he priciples of Eergy Field
More informationPrinciples of Communications Lecture 1: Signals and Systems. Chih-Wei Liu 劉志尉 National Chiao Tung University
Priciples of Commuicaios Lecure : Sigals ad Sysems Chih-Wei Liu 劉志尉 Naioal Chiao ug Uiversiy cwliu@wis.ee.cu.edu.w Oulies Sigal Models & Classificaios Sigal Space & Orhogoal Basis Fourier Series &rasform
More information12 Getting Started With Fourier Analysis
Commuicaios Egieerig MSc - Prelimiary Readig Geig Sared Wih Fourier Aalysis Fourier aalysis is cocered wih he represeaio of sigals i erms of he sums of sie, cosie or complex oscillaio waveforms. We ll
More informationEE3723 : Digital Communications
EE373 : Digial Communicaions Week 6-7: Deecion Error Probabiliy Signal Space Orhogonal Signal Space MAJU-Digial Comm.-Week-6-7 Deecion Mached filer reduces he received signal o a single variable zt, afer
More informationSubrings and Ideals 2.1 INTRODUCTION 2.2 SUBRING
Subrings and Ideals Chapter 2 2.1 INTRODUCTION In this chapter, we discuss, subrings, sub fields. Ideals and quotient ring. We begin our study by defining a subring. If (R, +, ) is a ring and S is a non-empty
More informationprobability of k samples out of J fall in R.
Nonparametric Techniques for Density Estimation (DHS Ch. 4) n Introduction n Estimation Procedure n Parzen Window Estimation n Parzen Window Example n K n -Nearest Neighbor Estimation Introduction Suppose
More information6.003 Homework #3 Solutions
6.00 Homework # Solutios Problems. Complex umbers a. Evaluate the real ad imagiary parts of j j. π/ Real part = Imagiary part = 0 e Euler s formula says that j = e jπ/, so jπ/ j π/ j j = e = e. Thus the
More informationUNIQUE FJORDS AND THE ROYAL CAPITALS UNIQUE FJORDS & THE NORTH CAPE & UNIQUE NORTHERN CAPITALS
Q J j,. Y j, q.. Q J & j,. & x x. Q x q. ø. 2019 :. q - j Q J & 11 Y j,.. j,, q j q. : 10 x. 3 x - 1..,,. 1-10 ( ). / 2-10. : 02-06.19-12.06.19 23.06.19-03.07.19 30.06.19-10.07.19 07.07.19-17.07.19 14.07.19-24.07.19
More informationGaussian source Assumptions d = (x-y) 2, given D, find lower bound of I(X;Y)
Gaussian source Assumptions d = (x-y) 2, given D, find lower bound of I(X;Y) E{(X-Y) 2 } D
More informationThermodynamic Variables and Relations
MME 231: Lecture 10 Thermodynamic Variables and Relations A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics Thermodynamic relations derived from the Laws of Thermodynamics Definitions
More informationGeneral Neoclassical Closure Theory: Diagonalizing the Drift Kinetic Operator
General Neoclassical Closure Theory: Diagonalizing the Drift Kinetic Operator E. D. Held eheld@cc.usu.edu Utah State University General Neoclassical Closure Theory:Diagonalizing the Drift Kinetic Operator
More informationEE456 Digital Communications
EE456 Digial Communicaions Professor Ha Nguyen Sepember 6 EE456 Digial Communicaions Inroducion o Basic Digial Passband Modulaion Baseband ransmission is conduced a low frequencies. Passband ransmission
More informationA First Course in Digital Communications
A Firs Course in Digial Communicaions Ha H. Nguyen and E. Shwedyk February 9 A Firs Course in Digial Communicaions /58 Block Diagram of Binary Communicaion Sysems m { b k } bk = s b = s k m ˆ { bˆ } k
More informationFundamentals of Thermodynamics. Chapter 8. Exergy
Fundamentals of Thermodynamics Chapter 8 Exergy Exergy Availability, available energy Anergy Unavailable energy Irreversible energy, reversible work, and irreversibility Exergy analysis : Pure Thermodynamics
More informationFinding small factors of integers. Speed of the number-field sieve. D. J. Bernstein University of Illinois at Chicago
The number-field sieve Finding small factors of integers Speed of the number-field sieve D. J. Bernstein University of Illinois at Chicago Prelude: finding denominators 87366 22322444 in R. Easily compute
More informationME 501A Seminar in Engineering Analysis Page 1
Seod ad igher Order Liear Differeial Equaios Oober 9, 7 Seod ad igher Order Liear Differeial Equaios Larr areo Mehaial Egieerig 5 Seiar i Egieerig alsis Oober 9, 7 Oulie Reiew las lass ad hoewor ppl aerial
More information" #$ P UTS W U X [ZY \ Z _ `a \ dfe ih j mlk n p q sr t u s q e ps s t x q s y i_z { U U z W } y ~ y x t i e l US T { d ƒ ƒ ƒ j s q e uˆ ps i ˆ p q y
" #$ +. 0. + 4 6 4 : + 4 ; 6 4 < = =@ = = =@ = =@ " #$ P UTS W U X [ZY \ Z _ `a \ dfe ih j mlk n p q sr t u s q e ps s t x q s y i_z { U U z W } y ~ y x t i e l US T { d ƒ ƒ ƒ j s q e uˆ ps i ˆ p q y h
More informationSTK4080/9080 Survival and event history analysis
STK48/98 Survival ad eve hisory aalysis Marigales i discree ime Cosider a sochasic process The process M is a marigale if Lecure 3: Marigales ad oher sochasic processes i discree ime (recap) where (formally
More informationExamination paper for TFY4240 Electromagnetic theory
Department of Physics Examination paper for TFY4240 Electromagnetic theory Academic contact during examination: Associate Professor John Ove Fjærestad Phone: 97 94 00 36 Examination date: 16 December 2015
More informationPROBLEMS AND SOLUTIONS 2
PROBEMS AND SOUTIONS Problem 5.:1 Statemet. Fid the solutio of { u tt = a u xx, x, t R, u(x, ) = f(x), u t (x, ) = g(x), i the followig cases: (b) f(x) = e x, g(x) = axe x, (d) f(x) = 1, g(x) =, (f) f(x)
More informationChapter 10. Laser Oscillation : Gain and Threshold
Chaper 0. aser Osillaio : Gai ad hreshold Deailed desripio of laser osillaio 0. Gai Cosider a quasi-moohromai plae wave of frequey propaai i he + direio ; u A he rae a whih
More informationThis document has been prepared by Sunder Kidambi with the blessings of
Ö À Ö Ñ Ø Ò Ñ ÒØ Ñ Ý Ò Ñ À Ö Ñ Ò Ú º Ò Ì ÝÊ À Å Ú Ø Å Ê ý Ú ÒØ º ÝÊ Ú Ý Ê Ñ º Å º ² ºÅ ý ý ý ý Ö Ð º Ñ ÒÜ Æ Å Ò Ñ Ú «Ä À ý ý This document has been prepared by Sunder Kidambi with the blessings of Ö º
More informationANSWER KEY WITH SOLUTION PAPER - 2 MATHEMATICS SECTION A 1. B 2. B 3. D 4. C 5. B 6. C 7. C 8. B 9. B 10. D 11. C 12. C 13. A 14. B 15.
TARGET IIT-JEE t [ACCELERATION] V0 to V BATCH ADVANCED TEST DATE : - 09-06 ANSWER KEY WITH SOLUTION PAPER - MATHEMATICS SECTION A. B. B. D. C 5. B 6. C 7. C 8. B 9. B 0. D. C. C. A. B 5. C 6. D 7. A 8.
More informationCOS 522: Complexity Theory : Boaz Barak Handout 10: Parallel Repetition Lemma
COS 522: Complexiy Theory : Boaz Barak Hadou 0: Parallel Repeiio Lemma Readig: () A Parallel Repeiio Theorem / Ra Raz (available o his websie) (2) Parallel Repeiio: Simplificaios ad he No-Sigallig Case
More information6.003: Signals and Systems
6.003: Sigals ad Sysems Lecure 8 March 2, 2010 6.003: Sigals ad Sysems Mid-erm Examiaio #1 Tomorrow, Wedesday, March 3, 7:30-9:30pm. No reciaios omorrow. Coverage: Represeaios of CT ad DT Sysems Lecures
More informationA Robust Adaptive Digital Audio Watermarking Scheme Against MP3 Compression
½ 33 ½ 3 Þ Vol. 33, No. 3 7 3 ACTA AUTOMATICA SINICA March, 7 è ¹ MP3 ß å 1, Ä 1 1 ý Â Åè ó ó ß Ì ß ñ1) Ä Ǒ ² ÂÔÅ þíò) û Ð (Discrete wavelet transform, DWT) Ð ßÙ (Discrete cosine transform, DCT) Í Í Å
More informationApplications of Light-Front Dynamics in Hadron Physics
Applications of Light-Front Dynamics in Hadron Physics Chueng-Ryong Ji North Carolina State University 1. What is light-front dynamics (LFD)? 2. Why is LFD useful in hadron physics? 3. Any first principle
More informationApplication of Combined Fourier Series Transform (Sampling Theorem)
Applicaion o Combined Fourier Serie ranorm Sampling heorem x X[] m m Sampling Frequency Deparmen o Elecrical and Compuer Engineering Deparmen o Elecrical and Compuer Engineering X[] x We need Fourier Serie
More informationAn Introduction to Optimal Control Applied to Disease Models
An Introduction to Optimal Control Applied to Disease Models Suzanne Lenhart University of Tennessee, Knoxville Departments of Mathematics Lecture1 p.1/37 Example Number of cancer cells at time (exponential
More informationMODERN CONTROL SYSTEMS
MODERN CONTROL SYSTEMS Lecure 9, Sae Space Repreeaio Emam Fahy Deparme of Elecrical ad Corol Egieerig email: emfmz@aa.edu hp://www.aa.edu/cv.php?dip_ui=346&er=6855 Trafer Fucio Limiaio TF = O/P I/P ZIC
More informationEECE 301 Signals & Systems Prof. Mark Fowler
EECE 31 Signals & Sysems Prof. Mar Fowler Noe Se #1 C-T Signals: Circuis wih Periodic Sources 1/1 Solving Circuis wih Periodic Sources FS maes i easy o find he response of an RLC circui o a periodic source!
More informationLet s express the absorption of radiation by dipoles as a dipole correlation function.
MIT Deparme of Chemisry 5.74, Sprig 004: Iroducory Quaum Mechaics II Isrucor: Prof. Adrei Tokmakoff p. 81 Time-Correlaio Fucio Descripio of Absorpio Lieshape Le s express he absorpio of radiaio by dipoles
More information7 Algebra. 7.1 Manipulation of rational expressions. 5x x x x 2 y x xy y. x +1. 2xy. 13x
7 Algera 7.1 Manipulation of rational expressions Exercise 7A 1 a x y + 8 x 7x + c 1x + 5 15 5x -10 e xy - 8 y f x + 1 g -7x - 5 h - x i xy j x - x 10 k 1 6 l 1 x m 1 n o 1x + 7 10 p x + a 7x + 9 (x +1)(x
More informationLA PRISE DE CALAIS. çoys, çoys, har - dis. çoys, dis. tons, mantz, tons, Gas. c est. à ce. C est à ce. coup, c est à ce
> ƒ? @ Z [ \ _ ' µ `. l 1 2 3 z Æ Ñ 6 = Ð l sl (~131 1606) rn % & +, l r s s, r 7 nr ss r r s s s, r s, r! " # $ s s ( ) r * s, / 0 s, r 4 r r 9;: < 10 r mnz, rz, r ns, 1 s ; j;k ns, q r s { } ~ l r mnz,
More information