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hwB28 - £ a b c a b c a b c a b c T S 28.2 P 3.27 in...

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ENEE 241 02 * HOMEWORK ASSIGNMENT 28 Due Wed 04/16 The signal x = £ 0 0 0 a b c 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 / T Express the following DFT’s in terms of the entries of X : (i) (5 pts.) The DFT X (1) of x (1) = £ a b c 0 0 0 a b c / T (ii) (5 pts.) The DFT X (2) of x (2) = £ a b c a b c a b c / T (iii) (5 pts.) The DFT X (3) of x (3) = £ a b c / T (iv) (5 pts.) The DFT X (4) of x (4) = £ a b c a b c / T Solved Examples S 28.1 ( 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 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 28.2 ( P 3.27 in textbook). In MATLAB notation, consider the 4-point vector
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Unformatted text preview: £ a b c a b c a b c a b c / T S 28.2 ( 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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