20072ee132A_1_hwk5

20072ee132A_1_hwk5 - and (c). 2. Problem 8.21 from Proakis...

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EE132A, Spring 2007 Communication Systems Prof. John Villasenor Handout # 12 TA: Choo Chin (Jeffrey) Tan Homework 5 Assigned: Monday, May 7, 2007 Due: Monday, May 14, 2007 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)
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Unformatted text preview: and (c). 2. Problem 8.21 from Proakis and Salehi. 3. Consider a set of signals: ≤ ≤ + = 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. 4. Design a likelihood ratio test to choose between: H 1 : p 1 (y) = 1/{(2 π ) 1/2 σ }exp[-y 2 /(2 σ 2 )]; -∞ < y < ∞ H : p (y) = 1/2 ; -1 < y < 1 H 1 and H 0 are the two hypotheses. Using MAP criterion, find out the decision regions in terms of y and as a function of σ 2 . Assume priori probabilities for H and H 1 to be equal. i = 1,2,3,4...
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This note was uploaded on 11/07/2009 for the course EE 132A taught by Professor Walker during the Spring '08 term at UCLA.

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