ENEE241hw07

# ENEE241hw07 - ENEE 241 02 HOMEWORK ASSIGNMENT 7 Due Tue...

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ENEE 241 02 * HOMEWORK ASSIGNMENT 7 Due Tue 03/29 Solve by hand (no inner products are needed). You may want to verify your answers on MATLAB. Problem 7A All vectors have length N =9 . (i) (4 pts.) The entries of the time-domain vector x (1) = ± 2 - 1 - 12 - 1 - - 1 - 1 ² T are given by 2 cos ωn ,whe re n = 0 : 8. What is the value of ω ?E x p r e s s x (1) as the sum of two Fourier sinusoids. By considering the appropriate column of the Fourier matrix V , determine and display the DFT X (1) . (ii) (4 pts.) Similarly, express the time-domain vector x (2) = ± 01 - 101 - - 1 ² T as a linear combination of the same two Fourier sinusoids as in part (i). Hence determine and display the DFT X (2) . (iii) (4 pts.) Determine and display the DFT X (3) of x (3) [ n ] = cos(2 πn/ 9) + 3 cos(4 9) ,n =0 ,..., 8 (iv) (4 pts.) Determine and display the DFT X (4) of x (4) [ n ]=s i n ( 8 9) 8 (v) (4 pts.) If the time-domain vector x (5) has DFT X (5) = ± 18 0 9 j 27 0 0 27 - 9 j 0 ² T write an equation for x (5) [ n ], where n = 0 : 8. Your equation should be in terms of cosines and sines.

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## This note was uploaded on 09/27/2011 for the course ENEE 241 taught by Professor Staff during the Spring '08 term at Maryland.

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ENEE241hw07 - ENEE 241 02 HOMEWORK ASSIGNMENT 7 Due Tue...

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