ece302hw4solns_Fa11

ece302hw4solns_Fa11 - Y _. a current — — Pr({%>1}) =...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Y _. a current — — Pr({%>1}) = Pr({Y > R}) = Pr({X > R}) since R>0 2 Pr({X > R}) = j ‘57; {Ea/x = Q(§) where Q(a) = L; e‘zx7dx =1~ (13(a) a 7! (b) p0wer=§ Y2 2 J1? PM? >1» = Pr({Y > R1) = Pr({X > m) = Q1?) (c) #1 = E1—E—1 = %E1Xu<X>1 = £fo (mix 1 °° 1 ~12 1 ~12 0' =- x e 2°“ dx= (*02)e 2" I”: RDI ° Jazz 50 \l27r0'R Y2 1 w 2 1 — xzz 1 2 '— X22 200 _ X22 E[— =— x e20 =————— —xo‘e2‘7 |°° +0' ezadx R2 R2 5‘- 27m' \/27r0'R2 0 5f x +y eon/2 r A2 = Tie— 2‘72 dxdy = I Je—firder = 0 0 0 0 2 0'7: 2 E[Y2]_ 0‘ XO_\/;_0'2 R2 427:1? 2 2R2 Y2 Y2 Y 2 0—2 1 02 =Var— =E——~(E—J = 1___ I [R2 72') Y2 1°° 1 if 02 d =E—— =— 2 lube:— <m 1R Rojx 2We 2R From E[(X~Y)4] = 30—4 and f = 0 2 °°41 x 34 2) Ix e_;2_dx=—0' 0 27:0 2 4 no _i 4 ML =L2 x4 1 R 0 27:0 2R 2R2 * 4R2 _ 4R2 Y4 Y4 Y2 2 304 a4 504 0%» = Vang] = E5; {ME-1] = z % 5 p’ i i i a _; é’ a E z s E /.,K “L my @2 (a) If the quantizer has K levels, then the ith interval will be x e (a+(i—1)>< (bfla),a+ix (b_a)],i=l,...,K K K When X is in that interval, the output Y = q(X) is equal to the midpoint of the interval. y : a+ (b—a)(21—-l) 2K (b) g(x) = x—q(x) —' In the ith interval, xe(a+(i—1)x(b—a),a+ix(b_a)j,i=1,...,K K K g(x)=x—[a+——-—————(b—az)§:i—D] (c) for general K Y = 900 _Ki _ M3532 fy(y)—§K5[y [01+ 2K E=g(X) fE(e):fX(x) = 0 ,else K ’EE[(a—b),(b—a)] fE(e): cal (anb><b—a> ;+...+fX(x) ,Ee[ 2K , 2K 92 de (b — a) 2K 2K 0 , else a+—11;(b—a) (d)E[E2]=jg(x)2fX(x)dx=K I (x_[a+b_a)] 1 dx _ K 1 x_((2K—~1)a+b]3 —(b—a)3 2K K b—a ((2K—1)a+b)]3 [ ((2K—1)a+b]]3} : a+ _ _ _ a_ ___.___.__ 3(b~a) K 2K 7 2K _ K (b~a)3_[a—bj3 _3(b—a) 2K 2K b—a a+—— K * (b—a)2 _" 2 é IEK ‘ ' mm :! Z g” ’ WW “" A 5 WW“??? ‘ «I M r ECQ1:\> $ 0 2”, a ’ w ‘ AwrM-hz’dz , Fr (Tub-(41L? s’f) : I‘ FTLX), : !- 045 ‘1’) Ce" / we” ‘6) WWW) = MT”) :61" “WWW 190%. , Pram) f w J 6521 Fr LT>~I D!) = = PFCTWJ’) ' a" : a" f '40 I 't ‘1’ . r L>Lo *0 f e kajrcbwnmo) = W ~ I Fran/o) $2” fa“? r 7." = 5a“ a Te” at h: :‘e 1 “Le— x610?) w 1“ * —eff +0106!) .% on m *5; :~Q{€ /¢" +£jx€ dd“— : f 1f :10 (f, EIMTmo] t 790‘.) Y“? fl (it L = » ~ 3 I e f" Hm) Pram) ~32?“ 9”” m» {TWO} = W701» alt ‘6 “Ag!” _.7? [afaroef :. ao‘dl" [4,016 W013] ‘ v a -3: t 7% PW”, 1‘ «’e I] 6* 4* .1 § -_ '= -{ I’ 06 w "E .73, I- Q. llo ‘1- 8 = *gz'rooe“ — m]: -e~:£;fl/(~j§)] _~(_’__" ~ ,1; co 4‘, ‘1‘ -7r[fooe wfb‘ffieflo'fjp erfl] Ii? ~ ¢fof:€"%d(_£)] .L t 7%: [$008u + {boa- e’ » *-——— tare : LO 7r( 0 J :»_ w; (EU-nu? ECTH>41= Elm f: -L r * ‘F * MT“) or T??? w" _ Mr "MI W 1W “MT?” grim“ uv pfip J.’ i“ ‘P T'Ol"-Iop“e rp‘ :- P 7 L& ‘MWDWIIQQ fro/e? EDITH} =§+w=mw -— “,‘f” = 9 ‘ w 0;?) ("WWW a. a PrUA‘+.lT1>"0): Pr<TWJ ‘4???” “(B/I Pr (flaw) /. I; (LJO’TJ ’ P 612:. _ : Ctr!) (Raf. 0‘84? Ly”) ‘: {£01. Pr(T‘_: $10} : “2&4. ...
View Full Document

This note was uploaded on 02/14/2012 for the course ECE 302 taught by Professor Gelfand during the Spring '08 term at Purdue.

Page1 / 9

ece302hw4solns_Fa11 - Y _. a current — — Pr({%>1}) =...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online