114_1_image_proc_exam_2008_Part1

# 114_1_image_proc_exam_2008_Part1 - 3 2D Unitary DFT(20...

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EE114D Introduction to Speech and Image Processing Winter Quarter, 2008 Page 1 of 3 Image Processing Exam Notes: - For all problems please circle or otherwise clearly indicate your answers! Note: 2 log 2 1 = , 2 5 log 3 3 , 2 log 4 2 = 2 7 log 5 3 , 2 17 log 7 6 The use of calculators or other electronic devices with calculator-like functionality is not permitted on this test. 1. 2D Convolution (20 points) Consider the continuous 2D function ) , f( y x given below, which has value 1 where the dark regions are located and 0 elsewhere. Make a sketch showing the boundaries of non-zero regions of the self-convolution of ) , f( y x . Be sure to place your sketch on a set of marked axis such that relevant dimensions and positions of features are clearly indicated. 2. Integration (20 points) Find the total area under the function ( 29 4 sin ( ) x f x x π =

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EE114D Introduction to Speech and Image Processing Winter Quarter, 2008 Page 2 of 3
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Unformatted text preview: 3. 2D Unitary DFT (20 points) Let the 2D unitary DFT of the 2D matrix Φ be Γ as indicated below. As is customary, the origin is the upper left element. 2 D DFT a b c d A B C D e f g h E F G H i j k l I J K L m n o p M N O P Φ = →Γ = Find the 2D unitary DFT of the matrix Ψ below in terms of the elements of Γ . k l i j o p m n c d a b g h e f Ψ = 4. 2D Unitary DCT (20 points) Find the unitary 2D inverse DCT of the following 8×8 matrix. As is customary, the (0,0) element is located in the upper left. 1 V =...
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114_1_image_proc_exam_2008_Part1 - 3 2D Unitary DFT(20...

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