Hw5 - UCSD ECE153 Prof Young-Han Kim Handout#18 Thursday Homework Set#5 Due Thursday May 5 2011 1 Neural net Let Y = X Z where the signal X U-1 1

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
UCSD ECE153 Handout #18 Prof. Young-Han Kim Thursday, April 28, 2011 Homework Set #5 Due: Thursday, May 5, 2011 1. Neural net. Let Y = X + Z , where the signal X U[ - 1 , 1] and noise Z ∼ N (0 , 1) are independent. (a) Find the function g ( y ) that minimizes MSE = E b (sgn( X ) - g ( Y )) 2 B , where sgn( x ) = ± - 1 x 0 +1 x > 0 . (b) Plot g ( y ) vs. y . 2. Additive shot noise channel. Consider an additive noise channel Y = X + Z , where the signal X ∼ N (0 , 1), and the noise Z |{ X = x } ∼ N (0 , x 2 ), i.e., the noise power of increases linearly with the signal squared. (a) Find E ( Z 2 ). (b) Find the best linear MSE estimate of X given Y . 3. Estimation vs. detection. Let the signal X = ² +1 , with probability 1 2 - 1 , with probability 1 2 , and the noise Z Unif[ - 2 , 2] be independent random variables. Their sum Y = X + Z is observed. (a) Find the best MSE estimate of X given Y and its MSE. (b) Now suppose we use a decoder to decide whether
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/07/2011 for the course EECS 153 taught by Professor Kim during the Spring '11 term at UCSD.

Page1 / 3

Hw5 - UCSD ECE153 Prof Young-Han Kim Handout#18 Thursday Homework Set#5 Due Thursday May 5 2011 1 Neural net Let Y = X Z where the signal X U-1 1

This preview shows document pages 1 - 2. Sign up to view the full document.

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