part21

# part21 - Univ Of Maryland at College Park ECE Department...

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Univ. Of Maryland at College Park, ECE Department ENEE324 Fall 2002 Instructor : M. Olfat Solution to Assignment #: 8 Posted on: 10/29/02 [ ] [ ] ( 29 1 0 1 0 10 2 Xm P P P ZQ s -  < = < = - ≥ = -=   [ ] [ ] X m PXm k k PX m k P k Pk sss ss -- - = - + - < - = + <- [ ] [ ] ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 1 12 P Zk P Q k Qk Q k Q k = + < - = + = +- 2 3 5 7 0.318 1 4.5 6 1 0 2 4.0 5 1 3 6.3 4 1 4 5.7 4 1 5 k k k k k - - - - = ×= = [ ] [ ] ( 29 1 3 5 7 1 1.28 1 3.09 1 4.26 1 5.2 k k k P k P k k s s - - - - = = - + = = == = = ( 29 2 x X f xe a a - = The quantizer is like the one in figure 3.15 page 120. Problem 2: [GAR]3.51 Problem 1: [GAR]3.44

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7 3 2 5 32 2 3 2 2 0 2 0 2 3 2 d xd d d d dxd d dx Y d d - <- - - ≤ <- - - -≤< = ≤< 2 5 23 2 7 3 2 d d So Y is a discrete r.v. with 75 3 357 ,, , , ,,, 22 2 22222 Y dd d ddddd S  = ----   Because of symmetry [ ] 3 3 7 71 3 2 222 d dd P Y P Y e d x e P Xd aa a - - -∞  == = - = = =   { } [ ] 2 3 5 51 2 d x d P Y P Y e d xe e P d a a - -- - = - = = - =-≤ ≤- { } [ ] 2 2 3 31 2 2 d x d P Y P Y e d e P dXd a a - - = - = = - { } [ ] 0 1 10 2 2 22 d P Y P Y e d x e PdX a - -   = = = - = = - = -≤<     Y a Xb =+
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part21 - Univ Of Maryland at College Park ECE Department...

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