L12 - 1 CMPEN/EE455 Lecture 12 Topics today 1 2-D Discrete Fourier Transform(DFT Pair 2 2-D DFT Properties periodicity 2-D Discrete Fourier

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Unformatted text preview: 1 CMPEN/EE455 Lecture 12 Topics today: 1. 2-D Discrete Fourier Transform (DFT) Pair 2. 2-D DFT Properties, periodicity 2-D Discrete Fourier Transform (DFT) Pair — G&W Ch. 4.5.5, 4.6; 1992 G&W Ch. 3.3 Discrete Fourier Transform (DFT): F ( u, v ) = M- 1 X x =0 N- 1 X y =0 f ( x, y ) e- j 2 π ( ux M + vy N ) , u = 0 , 1 , 2 , . . . M- 1 , and v = 0 , 1 , 2 , . . . N- 1 Inverse Discrete Fourier Transform (IDFT): f ( x, y ) = 1 MN M- 1 X u =0 N- 1 X v =0 F ( u, v ) e + j 2 π ( ux M + vy N ) , x = 0 , 1 , 2 , . . . M- 1 , and y = 0 , 1 , 2 , . . . N- 1 CMPEN/EE455 – Lect 12 2 Properties of 2-D DFT: Periodicity f ( x, y ) = f ( x + M, y + N ) F ( u, v ) = F ( u + M, v + N ) Shifting: f ( x- x o , y- y o ) ←→ F ( u, v ) e- j 2 π ( ux o ) M + ( vy o ) N Modulation: f ( x, y ) e j 2 π ( u o x ) M + ( v o y ) N ←→ F ( u- u o , v- v o ) Convolution: f ( x, y ) * g ( x, y ) ←→ F ( u, v ) G ( u, v ) A few more properties to follow.......
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This note was uploaded on 09/24/2009 for the course EE 455 taught by Professor Staff during the Fall '08 term at Pennsylvania State University, University Park.

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L12 - 1 CMPEN/EE455 Lecture 12 Topics today 1 2-D Discrete Fourier Transform(DFT Pair 2 2-D DFT Properties periodicity 2-D Discrete Fourier

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