l11 - 1 CMPEN/EE455 Lecture 11 Topics today: 1. Image...

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Unformatted text preview: 1 CMPEN/EE455 Lecture 11 Topics today: 1. Image Sampling and Mathematical development of DFT 2. The Whitaker-Shannon-Nyquist Sampling Theorem Image Sampling and the DFT: G&W Ch. 4.3-4.4; 1992 G&W Ch. 3.3.9 1. Sample a continuous image f ( x, y ) get sampled image f s ( x, y ) = f ( k x, l y ) Sampling Theorem 2. Given sampled image f s ( x, y ) { i.e., f ( k x, l y ) } meaning of processing only a finite segment of data, f h ( x )? aliasing phenomenon 3. Periodic extension of finite segment f p ( x ) tie to discrete domain reach Discrete Fourier Transform (DFT) CMPEN/EE455 Lect 11 2 Do 1-D development. Starting point: A general infinite extent image f a ( x ). End: a. understand all aspects of going to digital domain b. arrive at DFT *Three versions of development presented: 1) Block Diagram 2) Signal 3) Mathematical CMPEN/EE455 Lect 11 3 Image Sampling Version 1: Block Diagram Approach CMPEN/EE455 Lect 11 4 CMPEN/EE455 Lect 11 5 Image Sampling Version 2: Signal Approach CMPEN/EE455 Lect 11 6 Figs. 3.38-3.39 above are discussed in the 1992 G&W Chapter 3 excerpt, Section 3.3.9. CMPEN/EE455 Lect 11 7 Image Sampling Version 3: Mathematical Approach 1. Make f a ( x ) bandlimited new f ( x ) def.: f ( x ) is bandlimited if its Fourier transform satisfies:...
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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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l11 - 1 CMPEN/EE455 Lecture 11 Topics today: 1. Image...

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