sampling - Sampling Signal Sampling Lets sample the signal...

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1 ATMS 320 – Fal 2010 Signal Sampling Dr. Christopher M. Godfrey University of North Carolina Ashevil e Photo: C. Godfrey ATMS 320 – Fal 2010 Sampling Let’s sample the signal at a time interval of Δ t Analog Signal Δ t ATMS 320 – Fal 2010 Sampling Let’s sample the signal at a time interval of Δ t Analog Signal Samples at Δ t Δ t ATMS 320 – Fal 2010 Sampling Reconstruct the curve from the sampled points Analog Signal Samples at Δ t Δ t ATMS 320 – Fal 2010 Analog Signal Samples at Δ t Δ t Sampling High-frequency components in the curve are sampled poorly Low-frequency components in the curve are sampled well ATMS 320 – Fal 2010 Sampling ± Given that there can be sampling problems, what Δ t sampling interval should be selected in order to fully define the given input signal? ± We’ll look at a version of the sampling theorem to answer this… ² …but first, let’s review some properties of sines and cosines
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2 ATMS 320 – Fal 2010 Fourier Analysis ± Fourier analysis shows that any analog signal can be represented perfectly by an infinite sum of sines and cosines D1 Fourier Analysis ATMS 320 – Fal 2010 Great attributes of sine functions ± It’s possible to define a sine wave, with unity amplitude, using only two points (more is better)! ± For a given signal with multiple frequency components, we must find the largest sampling time interval ( Δ t s ), or lowest sampling frequency ( f s ) that will allow recovery of the signal without error ²
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This note was uploaded on 02/08/2012 for the course ITT 650 taught by Professor Dewey during the Spring '11 term at UNC Asheville.

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sampling - Sampling Signal Sampling Lets sample the signal...

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