Note #17_Sampling - Note 17. Sampling Read text, Sections...

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Note 17. Sampling Read text, Sections 7.1, 7.2, & 7.3. ( ) ( ) ( ) ? ) ( x t x t x t x t = Analog transducer, Sample Reconstruction r p voice,… Sampling frequency, T s π ω 2 = Basic Problem Can ( ) t x be represented uniquely by a sequence of equally spaced samples, ),. .. ( ),. .., 2 ( ), ( ), 0 ( nT x T x T x x
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Can () t x be represented uniquely by a sequence of equally spaced samples, ),. .. ( ),. .., 2 ( ), ( ), 0 ( nT x T x T x x ? Answer is , unless we either Æ sample faster (increase s ω ) t T 02 T 3 T Æ disallow fast-changing signals Make t x band-limited , i.e. , ( ) 0 = X for M ω> Examples: Æ voice Æ telephone
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Ideal Sampling (Impulse) () t x t () () () () ( ) ( ) −∞ = −∞ = = = = n n p nT t nT x nT t t x t p t x t x δ () ( ) −∞ = = n nT t t p ( ) t x t ( ) t x t
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Frequency Domain : () () () ( ) () ωω π ω P X X t p t x t x p p = = 2 1 ( ) X 1 ( ) limited - band M M 0 s 2 s s 2 s −∞ = = k s k T P δ 2 T 1 M s ω−ω M s + 0 s 2 s s 2 s −∞ = = = k s p k X T P X X 1 2 1
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Nyquist Sampling Criterion () limited - band t x ( ) x t p ( ) x t H ω r r ( ) t p T 1 ( ) p X 0 s 2 s s 2 s ( ) r X 1 M M c c Choose sampling frequency M s m s M 2 > < ( ) r H M s ω− M
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This note was uploaded on 05/03/2009 for the course ECSE 2410 taught by Professor Wozny during the Spring '07 term at Rensselaer Polytechnic Institute.

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Note #17_Sampling - Note 17. Sampling Read text, Sections...

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