114_1_image_proc_exam_solns_2008

114_1_image_proc_exam_solns_2008 - EE114D Winter Quarter,...

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EE114D Introduction to Speech and Image Processing Winter Quarter, 2008 Page 1 of 6 Image Processing Exam Solutions 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. Solution:
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Introduction to Speech and Image Processing Winter Quarter, 2008 Page 2 of 6 2. Integration (20 points) Find the total area under the function ( 29 4 sin ( ) x f x x π = Solution: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 { } ( 29 ( 29 ( 29 ( 29 { } ( 29 ( 29 ( 29 ( 29 4 2 4 2 2 2 2 2 1 1 2 3 0 0 sin ' : . . . . 2 2 2 1 1 3 3 total area under f x f x dx x dx x sinc x dx sinc x dx using Parseval s Theorem g x dx F T g x du here g x sinc x so F T g x rect u tri u du u du u +∞ -∞ +∞ -∞ +∞ +∞ -∞ -∞
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114_1_image_proc_exam_solns_2008 - EE114D Winter Quarter,...

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