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Unformatted text preview: 1 CMPEN/EE455 Lecture 14 Topics today: 1. Wraparound error in 2-D (circular) convolution using the DFT 2. Fast Fourier Transform (FFT) algorithm (G&W Ch. 4.11) 3 Example No zero padding Filter ( A B ) image f ( x, y ) with small ( C D ) operator g ( x, y ) symmetrical about origin (i.e., assume A >> C and B >> D ) Blindly use ( A B ) transforms to get h ( x, y ) = f ( x, y ) * g ( x, y ) (NOTE: This is very useful for filtering N N images with small mask [e.g., 3 3] filters avoids overhead of zero padding.) Question: What are good and bad points of h ( x, y )? CMPEN/EE455 Lect 14 2 f ( x, y ) = 0 outside x A- 1 and 0 y B- 1 nonzero only in an A B rectangle g ( x, y ) = 0 outside- C- 1 2 x C- 1 2 and- D- 1 2 y D- 1 2 nonzero only in a C D rectangle; assume C, D odd integers To do filtering, a. f e ( x, y ) = f ( x, y ) (We wont zero pad f ( x, y )!) b. Make g e ( x, y ) = A B zero-padded version of g ( x, y ) Requires special data organization; see NEXT PAGE!...
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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.
- Fall '08