hw16 - X : (i) The DFT Y of y = £ a b c 0 0 0 / T (ii) The...

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ENEE 241 02 * HOMEWORK ASSIGNMENT 16 Due Thu 04/16 The signal x = £ 0 0 0 0 0 0 a b c d 0 0 / T has DFT X given by X = £ D 0 D 1 D 2 D 3 D 4 D 5 D 6 D 7 D 8 D 9 D 10 D 11 / T The DFTs below should be expressed in terms of the entries of X . (i) (3 pts.) Determine the DFT X (1) of x (1) = £ a b c d 0 0 0 0 0 0 0 0 / T (ii) (4 pts.) Determine the DFT X (2) of x (2) = £ a b c d / T (iii) (4 pts.) Determine the DFT X (3) of x (3) = £ a b c d 0 0 / T (iv) (4 pts.) Determine the DFT X (4) of x (4) = £ a b c d a b c d / T (v) (5 pts.) Explain why the DFTs of x (5) = £ a b c d 0 0 0 0 / T and x (6) = £ a b 0 0 0 0 c d / T agree over all even-indexed entries, i.e., X (5) [ k ] = X (6) [ k ] for k = 0 , 2 , 4 , 6. Solved Examples S 16.1 ( P 3.26 in textbook). The twelve-point signal x = £ a b c 0 0 0 0 0 0 0 0 0 / T has DFT X given by X = £ X 0 X 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 X 9 X 10 X 11 / T Express the following DFT’s in terms of the entries of
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Unformatted text preview: X : (i) The DFT Y of y = £ a b c 0 0 0 / T (ii) The DFT S of s = £ a b c a b c a b c a b c / T S 16.2 ( P 3.27 in textbook). In MATLAB notation, consider the 4-point vector s = [a b c d].’ and its zero-padded extension x = [s ; zeros(12,1)] Let X denote the DFT of x . Express the DFT’s of the following vectors using the entries of X : x1 = s x2 = [ s ; s ] x3 = [ s ; s ; s ; s ; s ] % length=20 x4 = [ s ; z4 ] x5 = [ z4 ; s ] x6 = [ s ; z4 ; s ; z4 ] x7 = [ s ; s ; z4 ; z4 ] where z4 = zeros(4,1) ....
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This note was uploaded on 10/18/2011 for the course ENEE 241 taught by Professor Staff during the Spring '08 term at Maryland.

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hw16 - X : (i) The DFT Y of y = £ a b c 0 0 0 / T (ii) The...

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