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hw_chap1_3_solution

# hw_chap1_3_solution - UNIVERSITY OF CENTRAL FLORIDA SCHOOL...

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UNIVERSITY OF CENTRAL FLORIDA SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE EEL 3552 Signal Analysis and Communications Homework Question 1: Using a computer and whatever language to compute the capacity of the following AWGN channel. Figure 1: Spectrum of a telephone channel Suggested solutions:

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Matlab code to compute the first part: % Step 1 Create a Matlab M file named: firstpart.m function f = firstpart(t) f = log2(1+100/300*t); %Step 2: in matlab command window %Type the following command %len = quad(@firstpart,0,300) %answer is %len = % 1.5846e+003
Question 2: Compute Trigonometric Fourier series of -∞ = + = n n t x t y ) 2 ( ) ( and -∞ = + = n n t g t z ) ( ) ( , where x(t) and g(t) are given in the following Figure 1. Figure 3: Two signals Suggested solutions: y(t) is a periodic extension of x(t) with period To=2. -∞ = + = n n t x t y ) 2 ( ) ( Fundamental frequency π π ϖ = = o o T 2 Trigonometric Fourier series: = + + = 1 0 ) sin( ) cos( ) ( n n n t n b t n a a t y π π where 0 ) ( 2 1 1 1 0 = = - dt t y a 0 ) cos( ) 1 ( ) cos( 1 ) cos( ) ( 2 2 0 1 1 0 1 1 = - + = = - - dt t n dt

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