211A_1_Midterm2008

# 211A_1_Midterm2008 - Fall Quarter, 2008 Page 3 3. 2D...

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EE211A Digital Image Processing I Fall Quarter, 2008 Page 1 Midterm 1. 2D Convolution and Autocorrelation (25 points) Consider the continuous 2D function f(x,y) given below, which has value 1 where the dark regions are located and 0 elsewhere. (a) (14 points) Make a sketch showing the boundaries of non-zero regions of the function g(x,y) , where g(x,y) = f(x,y) * f(x,y) . Be sure to place your sketch on a set of marked axis such that relevant dimensions and positions of features of g(x,y) are clearly indicated. (b) (11 points) Make a sketch showing the boundaries of non-zero regions of the autocorrelation of f(x,y) . Again, your answer must be clearly indicated for you to receive credit.

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EE211A Digital Image Processing I Fall Quarter, 2008 Page 2 2. Integration (25 points) Evaluate the integral below. ( 29 sin 3 cos(2 ) t t dt t π -∞
EE211A Digital Image Processing I

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Unformatted text preview: Fall Quarter, 2008 Page 3 3. 2D Unitary DFT (25 points) Let the 2D unitary DFT of the 2D matrix be as indicated below. As is customary, the origin is the upper left element. 2 D DFT a b A B c d C D = = Find the 2D unitary DFT of the matrix below in terms of the elements of . = a b a b c d c d EE211A Digital Image Processing I Fall Quarter, 2008 Page 4 4. DCT (25 points) Find 2D unitary DCT of the matrix below: ( 29 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 u n =...
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## 211A_1_Midterm2008 - Fall Quarter, 2008 Page 3 3. 2D...

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