211A_1_Midterm2009

211A_1_Midterm2009 - EE211A Fall Quarter 2009 Digital Image...

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EE211A Digital Image Processing I Fall Quarter, 2009 Page 1 Midterm This test has five problems, 100 points total 1. 2D Convolution and Autocorrelation (20 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) (10 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. 2. 1D Fourier Transform (20 points) Find F ( u ) , the Fourier transform of the 1D function f ( x ) = δ ( x 2 - 1). You should express F ( u ) in its simplest form.
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EE211A Digital Image Processing I Fall Quarter, 2009 Page 2 3. 3D Linear, Shift-invariant Systems (20 points) Consider a linear, shift invariant system described by the following 3D (not 2D) difference equation: ( , , ) ( 1, , ) ( , 1, ) ( , 1,
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211A_1_Midterm2009 - EE211A Fall Quarter 2009 Digital Image...

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