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MIT6_003S10_lec21_handout

MIT6_003S10_lec21_handout - 6.003 Signals and Systems...

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6.003: Signals and Systems 6.003: Signals and Systems Sampling April 27, 2010 Sampling Conversion of a continuous-time signal to discrete time. x ( t ) x [ n ] Lecture 21 April 27, 2010 Mid-term Examination #3 Tomorrow: Wednesday, April 28, 7:30-9:30pm. No recitations tomorrow. Coverage: Lectures 1–20 Recitations 1–20 Homeworks 1–11 Homework 11 will not collected or graded. Solutions are posted. Closed book: 3 pages of notes ( 8 1 2 × 11 inches; front and back). Designed as 1-hour exam; two hours to complete. Sampling Sampling allows the use of modern digital electronics to process, record, transmit, store, and retrieve CT signals. audio: MP3, CD, cell phone pictures: digital camera, printer video: DVD everything on the web n t 0 2 4 6 8 10 0 2 4 6 8 10 We have used sampling a number of times before. Today: new insights from Fourier representations. Sampling Sampling is pervasive. Example: digital cameras record sampled images. x y I ( x, y ) m n I [ m, n ] Sampling Photographs in newsprint are “half-tone” images. Each point is black or white and the average conveys brightness. 1
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6.003: Signals and Systems Lecture 21 April 27, 2010 Sampling Sampling Zoom in to see the binary pattern. Even high-quality photographic paper records discrete images. When AgBr crystals ( 0 . 04 1 . 5 μ m) are exposed to light, some of the Ag is reduced to metal. During “development” the exposed grains are completely reduced to metal and unexposed grains are removed. Images of discrete grains in photographic paper removed due to copyright restrictions. Sampling Every image that we see is sampled by the retina, which contains 100 million rods and 6 million cones (average spacing 3 μ m) which act as discrete sensors. http://webvision.med.utah.edu/imageswv/sagschem.jpeg Courtesy of Helga Kolb, Eduardo Fernandez, and Ralph Nelson. Used with permission .
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