ECE108HW%236sol_06

# ECE108HW%236sol_06 - ECE 108 Hw#6 Due Solution 1 Problem...

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ECE 108 Hw#6 — Due 3/20/06 Solution 1. Problem 3.13 Given () sin 4 Hj ω = The output Fourier coefficients are given by 0 kk YX H j k = To find these coefficients it is necessary to determine the coefficients of the x(t) . Then 000 00 0 0 0 0 0 84 8 4 4 8 0 4 48 4 0 4 4 4 4 0 11 1 88 8 1 1 8 1 21 2 22 8 jk t jk t jk t k jk t jk t jk jk jk jk jk jk jk jk jk Xx t e d t e d t e d t ee jk jk e jk e e e jk jk e jk ωωω ωω −−− −− == =− +  − − +  ∫∫ [] 0 cos 4 1 cos 1 1 1(1 ) 1 1 j k k k e kj k k jj π ωπ = Now to find the output coefficients

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2 () ( ) () ( ) 22 sin 12 1 11 8 82 4 s i n kk k k k Yj H j k j k j k k π ππ   =− =    But sin( ) 0 k = Therefore 0 k Y = 2. Given the Amplitude and Phase Spectrum of a discrete-time signal x ( n ) as follows Determine the signal x ( n ). 73 24 2 4 2 2 35 3 5 44 4 4 1111 4422 33 1 4 4 jj n n n n n n jn j n n x n ee e e e e e j j e e π π −− + + =+++ ++ + −−− =+ + + + Next observe 735 3 4 4 , j n j nj n j n j n
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ECE108HW%236sol_06 - ECE 108 Hw#6 Due Solution 1 Problem...

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