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114_1_image_proc_exam_2010_Part1

# 114_1_image_proc_exam_2010_Part1 - EE114 Winter Quarter...

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EE114 Introduction to Speech and Image Processing Winter Quarter, 2010 Page 1 of 4 EE114 Image Processing Exam Notes: - For all problems please circle or otherwise clearly indicate your answers! The use of calculators or other electronic devices with calculator-like functionality is not permitted on this test. 1. 2D DFT (25 points) Find the forward 2D unitary DFT ) , ( l k v of the following matrices. The origin (in other words, the (0,0) element), is in the upper left corner. a) (12 points) 0 0 0 0 0 0 0 0 ( , ) 4 0 0 0 0 1 1 1 1 u m n = b) (13 points) 1 1 1 1 1 ( , ) 1 1 4 1 1 j j j j u m n j j j j - - - - = - - - - .

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EE114 Introduction to Speech and Image Processing Winter Quarter, 2010 Page 2 of 4 2. 2D DFT Symmetries (25 points) Consider a 2D real sequence ) , ( n m u of size 4 × 4 whose DFT ) , ( l k v has been determined. Suppose that these data were stored on computer, and that a careless colleague has accidentally erased ), , ( n m u as well as several of the elements of ). , ( l k v Nine of the 16 elements of ) , ( l k v were not erased and are indicated below by the letters A through I. These letters may in general
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