20111ee114_1_hw6

20111ee114_1_hw6 - 3,3 2,2 0,0 , , A A A for the N = 4 2-D...

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EE114, Winter 2011 Problem Set 6 ________________________________________________________________________ Problem Set #6 Due: February 28, 2011 1) (a) As discussed in lecture, the four basis vectors of the N = 4 1-D DFT form an orthonormal set, that is , a a k l k l = = 1 0 , , , , otherwise where * denotes complex conjugation. Confirm that the above relationship holds for the four possible combinations of k and l = 0 or 1 (e.g. k,l = 0,0; 0,1; 1,0; and 1,1). (b) Determine the basis images
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Unformatted text preview: 3,3 2,2 0,0 , , A A A for the N = 4 2-D DFT. (c) Find the inverse 2-D DFT of the matrix V = 1 1 1 V . (d) Confirm that the inverse 2-D DFT computed in c) is the sum of the three basis images found in b). 2) Find the 2-D unitary DCT of the following matrix: = 1 1 1 1 1 1 U...
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