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20111ee114_1_hw6_sol

# 20111ee114_1_hw6_sol - for the N = 4 2-D DFT Recall Thus...

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EE114, Winter 2011 Problem Set 6 Solution ________________________________________________________________________ Problem Set #6 Solution 1) a) Confirm that the four basis vectors of the N = 4 1-D DFT form an orthonormal set, that is, where, * denotes 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). Here, the dot in means dot product (or inner product). The basis vectors are Now we show they are orthonormal.

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EE114, Winter 2011 Problem Set 6 Solution ________________________________________________________________________ 1) b) Determine the basis images

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Unformatted text preview: for the N = 4 2-D DFT. Recall, . Thus, EE114, Winter 2011 Problem Set 6 Solution ________________________________________________________________________ 1) c) Find the inverse 2-D DFT of the matrix V d) Confirm that the inverse 2-D DFT computed in c) is the sum of the three basis images found in b) . This is the same as the result of part c) EE114, Winter 2011 Problem Set 6 Solution ________________________________________________________________________ 2) Find the 2-D unitary DCT of the following matrix: . Since our 2-D DCT is unitary we have , where, So, Doing the matrix multiplication, we get...
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20111ee114_1_hw6_sol - for the N = 4 2-D DFT Recall Thus...

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