211A_1_final2008solution

211A_1_final2008solution - EE211A Fall Quarter, 2008...

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EE211A Digital Image Processing I Fall Quarter, 2008 1 Final Exam Solutions 1. 2D DFT (20 points) The above 128x128 image consists of two equal amplitude sinusoids added to a gray background. The intensity of the background before the addition of the sinusoids was 0.5. As usual, 0 represents black and 1 is white. Find the location of the non-zero elements in the two-dimensional Fourier transform of the above image. Answer: The image consists of two diagonal sinusoids and a DC component. We can count the number of cycles in the vertical and horizontal direction to determine the frequency of the sinusoids. The low frequency sinusoid has 4 complete cycles in the vertical direction and 0 cycles in the horizontal direction. ). This corresponds to frequency 4. The high frequency sinusoid has 8 complete cycles in each direction, so this corresponds to frequency 8. (k,l) => (0,0),(4,0),(-4,0),(8,8),(-8,-8)
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EE211A Digital Image Processing I Fall Quarter, 2008 2
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EE211A Digital Image Processing I Fall Quarter, 2008 3 2. SVD Transform (20 points) For this problem consider the 4 × 4 matrix U given as follows: 1 0 0 2 0 1 0 0 0 0 2 0 1 0 0 2 U = Perform the SVD decomposition on the matrix U . For your answer, specify (as numbers, not as expressions or equations) all of the elements of each of the three matrices 1/ 2 , , and T Ψ Λ Φ
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211A_1_final2008solution - EE211A Fall Quarter, 2008...

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