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Re-constructing the analog data (signals)

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• Re-constructing the analog data from the samples: Lagrange inter-polation
  • Fact: (from Mathematics)

    You can construct a unique polynomial function of degree n−1 that passes through exactly n points Examples: The dotted plot is the original signal

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  • Langrange Polynomial:

    Langrange Polynomial = the polynomial function (of degree n−1) that you can construct when given exactly n data points See Wikipedia for more details: click here

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  • Re-constructing the analog data from the digital signal:

    The digital signals (pulses) is first converted back to digital values: A Interpolation Polynomial is computed using n data points at a time

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  • Try it out:

    Here's a nice Language Polynomial applet that you can play with: click here I downloaded a less nicer one: click here Check out the /home/cs455000/demo/Langrange directory