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20105ee211A_1_HW1Solutions

# 20105ee211A_1_HW1Solutions - y x When both x and y are...

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1 EE 211A Digital Image Processing I Fall Quarter, 2010 Handout 5 Instructor: John Villasenor Homework 1 Solutions 1. (a) = ) , ( y x f rect ) ( ) ( ) , ( ) ( 2 1 y f x f y x f b ax = + where = 1 f rect ) ( b ax and . 1 ) ( 2 = y f ) , ( v u F = ), ( ) ( 2 1 v F u F rect ) ( b ax → 1 1 ( ) | | F u a = sinc , 2 u a b j e a u π 1 → ) ( ) ( 2 v F v = δ | | 1 ) , ( a v u F = sinc ) ( 2 v e a u u a b j δ π (b) Use FT property that . 1 ) ( a u F a ax f ) ( 2 2 ax f e e x b bx = = - - π π where π b a = 2 2 2 . b u x b e e b π π π π - - ←→ b u e b v u F 2 2 ) , ( π π - = rect ) ( v

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2 2. The region of nonzero autocorrelation is: y x 3. The function ) , ( y x g has a value given by the area of overlap of two unit squares
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Unformatted text preview: ). , ( y x When both x and y are displaced simultaneously, as occurs along the line , x y = the x dimension and y dimension of the area of overlap will decrease linearly, leading to a quadratic overall decrease in ). , ( y x g The maximum value of ) , ( y x g will occur at ), , ( where there is complete overlap between the two unit squares. At this location, ) , ( y x g will have value 1....
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20105ee211A_1_HW1Solutions - y x When both x and y are...

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