hwB21 - j-j / T , where j 2 =-1 as usual. The equation for...

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ENEE 241 02* HOMEWORK ASSIGNMENT 21 Due Fri 03/28 Solve without using MATLAB, except to verify your results. All vectors have length N = 10 . (i) (4 pts.) The time-domain vector x (1) has DFT X (1) = £ 0 1 0 0 0 0 0 0 0 1 / T Which two Fourier frequencies ω does x (1) contain? By considering the appropriate columns of the Fourier matrix V , determine and display the vector x (1) . (ii) (4 pts.) If the time-domain vector x (2) has DFT X (2) = £ 0 0 0 0 1 0 0 0 0 0 / T write an equation for x (2) [ n ], where n = 0 ,..., 9. (iii) (4 pts.) Repeat for X (3) =
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Unformatted text preview: j-j / T , where j 2 =-1 as usual. The equation for x (3) [ n ] should not contain j , i.e., x (3) [ n ] is real-valued. (iv) (4 pts.) Repeat for X (4) = 1 0 5 j-5 j 1 / T (v) (4 pts.) Without computing any inner products, display the DFT X (5) of the vector given by the equation x (5) [ n ] = 4-cos(2 n/ 5)-7cos(3 n/ 5) , n = 0 ,..., 9...
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