hw12 - determine and display the DFT X (2) . (iii) (4 pts.)...

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ENEE 241 02 * HOMEWORK ASSIGNMENT 12 Due Thu 04/02 Solve by hand (no inner products are needed). You may want to verify your answers on MATLAB. All vectors have length N = 12 . (i) (4 pts.) The time-domain vector x (1) = £ 1 - 1 1 - 1 1 - 1 1 - 1 1 - 1 1 - 1 / T is a Fourier sinusoid. What is its frequency ω ? By considering the appropriate column of the Fourier matrix V , determine and display the DFT X (1) . (ii) (4 pts.) Express the time-domain vector x (2) = £ 0 1 0 1 0 1 0 1 0 1 0 1 / T as a linear combination of x (1) (above) and another easily identifiable Fourier sinusoid. Hence
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Unformatted text preview: determine and display the DFT X (2) . (iii) (4 pts.) Determine and display the DFT X (3) of x (3) [ n ] = 3cos( n/ 3)-cos(5 n/ 6) , n = 0 ,..., 11 (iv) (4 pts.) Using the formula e j-e-j = 2 j sin , determine and display the DFT X (4) of x (4) [ n ] = sin(2 n/ 3) , n = 0 ,..., 11 (v) (4 pts.) If the time-domain vector x (5) has DFT X (5) = 1 4-8 j-9 3-9 8 j 4 / T write an equation for x (5) [ n ], where n = 0 ,..., 11....
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