211A_1_Midterm2010

211A_1_Midterm2010 - EE211A Fall Quarter 2010 Digital Image...

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EE211A Digital Image Processing I Fall Quarter, 2010 Page 1 Midterm Note that a n n = 0 N 1 = 1 a N 1 a 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) (15 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) (10 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, 2010 Page 2 2. Summation (25 points) Use the Fourier transform relationships given in the problem statement below to evaluate the following summation: sinc 2 ( ) n = 1 You may find the following information useful for this problem.
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211A_1_Midterm2010 - EE211A Fall Quarter 2010 Digital Image...

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