MIT6_003S10_lec21

MIT6_003S10_lec21 - 6.003: Signals and Systems Sampling...

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6.003: Signals and Systems Sampling April 27, 2010
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Mid-term Examination #3 T om orrow: W ednesday, A pril 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. 1 Closed book: 3 pages of notes ( 8 × 11 inches; front and 2 back). Designed as 1-hour exam; two hours to complete.
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Sampling Conversion of a continuous-time signal to discrete time. x ( t ) x [ n ] n t 0 2 4 681 0 02 4 0 We have used sampling a number of times before. Today: new insights from Fourier representations.
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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
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Sampling Sampling is pervasive. Example: digital cameras record sampled images. y I ( x,y ) n I [ m,n ] x m
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Sampling Photographs in newsprint are “half-tone” images. Each point is black or white and the average conveys brightness.
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Sampling Zoom in to see the binary pattern.
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Sampling 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 completely reduced to metal and unexposed grains removed. Images of discrete grains in photographic paper removed due to copyright restrictions.
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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. Courtesy of Helga Kolb, Eduardo Fernandez, and Ralph Nelson. Used with permission. http://webvision.med.utah.edu/imageswv/sagschem.jpeg
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Check Yourself Your retina is sampling this slide, which is composed of 1024 × 768 pixels. Is the spatial sampling done by your rods and cones ade- quate to resolve individual pixels in this slide?
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Check Yourself The spacing of rods and cones limits the angular resolution of your retina to approximately rod/cone spacing 3 × 10 6 m θ eye = diameter of 3 cm 10 4 radians The angle between pixels viewed from the center of the classroom is approximately screen size / 1024 3 m / 1024 3 × 10 4 radians θ pixels = distance to screen 10 m Light from a single pixel falls upon multiple rods and cones.
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Sampling How does sampling affect the information contained in a signal?
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Sampling We would like to sample in a way that preserves information, which may not seem possible. x ( t ) t Information between samples is lost. Therefore, the same samples can represent multiple signals. cos 7 3 π n ? cos π 3 n ? t
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Sampling and Reconstruction To determine the effect of sampling, compare the original signal x ( t ) to the signal x p ( t ) that is reconstructed from the samples x [ n ] .
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This note was uploaded on 12/14/2011 for the course EE 6.003 taught by Professor Freeman during the Fall '11 term at MIT.

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MIT6_003S10_lec21 - 6.003: Signals and Systems Sampling...

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