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Sampling rate and accuracy --- the Nyquist rate

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• Sampling rate and accuracy of the reconstructed analog signal

  • Re-constructed signal and the original signal using a low sampling rate:

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  • Re-constructed signal and the original signal using a higher sampling rate:

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  • Conclussion:

    The faster (more frequent) you sample, the more accurate the approximation

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  • $64,000 question:

    Should we sample as fast as possible ????

    No !!!! The reason is cost !!

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• Transmission rate
  • Transmission rate:

    Transmission rate = the amount of data (in bits) transmitted per time unit (sec)

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  • Fact:

    We should try to keep the transmission rate as low as possible (More data sent = higher cost)

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• Sampling rate and transmission rate
  • Data rate at a low sampling rate:

    Conclusion:

    We only need to sent 5 values when we sample at the lower sampling rate

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  • Data rate at a higher sampling rate:

    Conclusion:

    We must sent 9 values when we sample at the higher sampling rate !!!!

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  • Therefore:

    The faster (more frequent) you sample, the higher the (transmission) data rate

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• What is the best sampling rate ???
  • High sampling rate:

    Good accuracy High transmission data rate (costly)

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  • Low sampling rate:

    Poor accuracy Low transmission data rate (cost-efficient)

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  • Goal: (what we want)

    At which data rate can we achieve good enough accuracy ????

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• The Nyquist Sampling Rate
  • The Nyquist (sampling) rate:

    Nyquist (sampling) rate = the minimum sampling rate required to avoid aliasing when sampling a continuous signal. See: Wikipedia Aliasing: an effect that causes different signals to become indistinguishable when sampled. See: Wikipedia

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  • In plain English:

    Nyquist rate = the lowest possible sampling rate that permits an accurate reconstruction of a input signal using samples

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  • Disclaimer:

    We will not derive the Nyquist rate :-)... because it requires a lot of background knowledge and is beyond the scope of this course...

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  • I will only state the result from Signal Processing:

    Nyquist Rate = 2 × B where: B = highest frequency found in the (analog) input signal