20091ee114_1_hw5_sol

20091ee114_1_hw5_sol - EE114, Winter 2009 Problem Set 5...

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EE114, Winter 2009 Problem Set 5 Solution ________________________________________________________________________ Problem Set #5 Solution 1) Let f(x,y) be a function below with value 1 in the shaded region and 0 otherwise. a) Give a sketch of f(x,-y) b) Give a sketch of f(-x,-y) flip f(x,y) with respect to the x-axis flip f(x,y) with respect to the origin x y f(x,y) x y f(x,-y) x y f(-x,-y)
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EE114, Winter 2009 Problem Set 5 Solution ________________________________________________________________________ 2) Find the 2D Fourier Transform of the two-dimensional function f(x,y) ( 29 ( 29 ( 29 ( 29 ( 29 { } ( 29 { } ( 29 { } ( 29 ( 29 . . , ( ) ( ) in otherwords, this is a separable function so we can find the F.T.of each dimension separately . . , . . . . ( ) ( ) ( F T f x y rect ax b sinc cy b rect a x sinc cy a g x h y F T f x y F T g x F T h y G u H v first find G u rect x sinc u = + = + = = = ←→ ( 29 ( 29 ( 29 ( 29
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20091ee114_1_hw5_sol - EE114, Winter 2009 Problem Set 5...

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