211A_1_Midterm2006Solutions

# 211A_1_Midterm2006Solutions - EE211A Fall Quarter, 2006...

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EE211A Digital Image Processing I Fall Quarter, 2006 Page 1 Midterm Solutions 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. Answer:

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EE211A Digital Image Processing I Fall Quarter, 2006 Page 2 (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. Answer:
EE211A Digital Image Processing I Fall Quarter, 2006 Page 3 2. 2D Linear Systems (20 points) Consider a system described by the following 2D difference equation: y(m, n) = y(m-1, n) + y(m-2, n-1) + y(m-2, n+1) + x(m, n). (a) (10 points) Find and show the output of the impulse response h(m,n) of the 2D system. Your answer must include the points in range 0 m 5 and -5 n 5 and must clearly specify values of nonzero outputs. Answer: (b) (10 points) Find the value of the impulse response h(m,n) at the location (m=16,n=7). Your answer should be a number, not an equation. Answer: y(2k,k)=1 for non-negative integer k. y(2k+1,k) = y(2k,k) + y(2k-1,k-1)+y(2k-1,k+1) = 1 + y(2(k-1)+1,k-1) Since y(1,0)=1, y(2k+1,k)=k+1 y(2k+2,k) = y(2k+1,k)+y(2k,k-1)+y(2k,k+1) = k+1 + y(2k,k-1) y(16,7) = 8+y(14,6)=8+7+y(12,5)=8+7+6+y(10,4)=…=8+7+6+5+4+3+2+y(2,0)=36

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## This note was uploaded on 04/18/2011 for the course EE 211A taught by Professor Villasenor during the Fall '10 term at UCLA.

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211A_1_Midterm2006Solutions - EE211A Fall Quarter, 2006...

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