13 - MEEN260 IntroductiontoEngineering Experimentation...

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MEEN 260 Introduction to Engineering xperimentation Experimentation Sampling Theory Reza Langari* Department of Mechanical Engineering Texas A&M University angari@tamu.edu rlangari@tamu.edu *Incorporates one or more slides from Brian Rasmussen, TAMU MEEN, Copyright 2008.
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nalog and Digital Signals Analog and Digital Signals When we take a measurement from an analog sensor, we need to convert it to digital form nalog to Digital nalog signal : What happens during the conversion? Analog to Digital Converter (ADC) Analog signal Digital signal Q: What happens during the conversion? Sampling and Quantization x ( t ) x s [ n ] Δ Δ t n 1 5 2 4 3 6
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mpling Sampling Sample the previous signal Sampling is like taking ‘snapshots’ in time x [ n ] n We assume the sampling occurs at fixed intervals of time 1 5 2 4 3 6 Sample time: (e.g. 0.1 sec) The sampled signal has the same value as the original analog signal at every th instant in time: s T T ) ( ] [ s nT x n x = s
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uantization Quantization oring the sampled signal Storing the sampled signal Unfortunately, computers can’t store the exact sampled values (they have finite precision) The stored numbers are approximations of the actual values 0 x x Real No. Line 0 h f th di it l il l b Δ A/D Conv. The accuracy of the digital signal can only be within Δ of the real signal
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uantization Quantization The “rounding” of sampled signal values is termed quantization Level of quantization affects accuracy More bits mean more accuracy e.g. 8 bit vs. 16 bit vs. 32 bit micro processors. g p x Q ( t ) Δ Δ Basically, we may not be able to capture elements of the signal that lie between information quanta. t
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uantization xample (JPEG quantization) Quantization Example (JPEG quantization) 43K 13K 3.5K Smaller file size means more quantization.
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mpling Theory Sampling Theory How does sampling affect our signal?
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This note was uploaded on 12/26/2010 for the course MEEN 260 taught by Professor Langari during the Fall '08 term at Texas A&M.

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13 - MEEN260 IntroductiontoEngineering Experimentation...

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