114_1_image_proc_exam_solns_2010_Part1

# 114_1_image_proc_exam_solns_2010_Part1 - EE114 Winter...

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Introduction to Speech and Image Processing Winter Quarter, 2010 Page 1 of 6 EE114 Image Processing Exam Solutions 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 = Solution: b) (13 points) 1 1 1 1 1 ( , ) 1 1 4 1 1 j j j j u m n j j j j - - - - = - - - - Solution: This is a complex corrugation in the diagonal direction. We expect that its DFT will contain only 1 nonzero component. row DFT column DFT 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 4 ( , ). 0 0 0 0 0 0 0 0 4 0 0 0 1 1 1 1 2 0 0 0 4 0 0 0 j v k l j → → = - -

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114_1_image_proc_exam_solns_2010_Part1 - EE114 Winter...

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