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

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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 Δ x, l Δ y ) Sampling Theorem 2. Given sampled image f s ( x, y ) { i.e., f ( k Δ x, l Δ 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)

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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

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CMPEN/EE455 – Lect 11 4
CMPEN/EE455 – Lect 11 5 Image Sampling — Version 2: “Signal” Approach

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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

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