20092ee132A_1_hwk5

# 20092ee132A_1_hwk5 - + = elsewhere T t i t f T E t s c i ;...

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EE132A, Spring 2009 Communication Systems Prof. John Villasenor Handout # 12 TA: Pooya Monajemi and Erica Han Homework 5 Assigned: Monday, May 4, 2009 Due: Monday, May 11, 2009 Reading Assignment: chapter 8 (8.1 to 8.5) 1. Consider the set of signals + = elsewhere T t i t f T E t s c i ; 0 0 ); 4 2 cos( 2 ) ( π where i = 1, 2, 3, 4, and f c = n c /T for some fixed integer n c . (a) What is the dimensionality, N, of the space spanned by this set of signals? (b) Find a set of orthonormal basis functions to represent this set of signals. (c) Using the expansion, = = N j j ij i t s t s 1 ) ( ) ( ϕ Find the coefficients s ij . (d) Plot the locations of s i (t), i = 1, 2, 3, 4, in the signal space, using the results of parts (b) and (c). 2. Problem 8.21 from Proakis and Salehi. 3. Consider a set of signals:

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Unformatted text preview: + = elsewhere T t i t f T E t s c i ; ); 4 2 cos( 2 ) ( where i=1,3,5,7. Calculate the union bound on symbol error probability, P e. i = 1,2,3,4 4. Consider two hypotheses H and H 1 under which a random variable y will have different PDFs , given respectively as follows: ( ) ( ) 2 1 1 2 2 1 : exp , 2 2 1 : , 1 1 2 y H p y y H p y y = < < = < Design a likelihood ratio test to choose between H and H 1 given a realization y. Using MAP criterion, find out the decision regions in terms of y and as a function of 2 . Assume priori probabilities for H and H 1 to be equal....
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## This note was uploaded on 02/05/2012 for the course EE 132B taught by Professor Izhakrubin during the Spring '09 term at UCLA.

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20092ee132A_1_hwk5 - + = elsewhere T t i t f T E t s c i ;...

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