l6 - 1 CMPEN/EE485 Lecture 6 Topics today 1(G&W Ch 4...

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1 CMPEN/EE485 Lecture 6 Topics today: 1. (G&W Ch. 4) Introduction to Frequency-Domain Analysis 2. (G&W Ch. 4.2; 1992 G&W Ch. 3.1, 3.3) Review 1-D Fourier Transform The Frequency Domain and Image Filtering — a. G&W, Chapter 4 — b. Old G&W, Chapter 3, pp. 81-119, 1992 (1st) edition. 1. Continuous 1-D Fourier transform (Ch. 4.2, 4.5; 1992 Ch. 3.1, 3.3) 2. Continuous 2-D Fourier transform 3. Sampling of Continuous-Space Images (Ch. 4.3 - 4.5; 1992 Ch. 3.3.9) a. continuous ( x, y ) -→ discrete sampled ( x, y ) b. infinite extent f ( x, y ) -→ truncated f ( x, y ) 4. Discrete Fourier Transform (DFT) (Ch. 4.4-4.7, 4.11; 1992 Ch. 3.3) a. properties b. circular convolution (filtering) c. Fast Fourier Transform (FFT) algorithm for DFT 5. Filtering (Ch. 4.8, 4.9)
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CMPEN/EE455 – Lect 6 2 Uses of Fourier (Transform) Analysis 1.) Understanding spatial sampling from continuous to discrete (digital) domain 2.) Filter images using linear filters (e.g., lowpass, highpass) 3.) Analyze (linear) mask operators (G&W Ch. 3 and 10) 4.) JPEG and MPEG image compression * Most of the semester (parts 2-4 above), we use the DFT.
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CMPEN/EE455 – Lect 6 3
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