This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: UCSD ECE153 Handout #18 Prof. YoungHan 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 bracketleftbig (sgn( X ) g ( Y )) 2 bracketrightbig , where sgn( x ) = braceleftBigg 1 x +1 x > . (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 = braceleftbigg +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....
View Full
Document
 Spring '08
 staff

Click to edit the document details