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Ensemble Averaging

  • Page ID
    77546
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    Ensemble averaging is a data acquisition method that enhances the signal-to-noise of an analytical signal through repetitive scanning. Ensemble averaging can be done in real time, which is extremely useful for analytical methods such as:

    • Nuclear Magnetic Resonance Spectroscopy (NMR)
    • Fourier Transform Infrared Spectroscopy (FTIR)
    • Near-Infrared (NIR) Spectrophotometry
    • UV-Visible Spectrophotometry

    Ensemble averaging also works well with multiple datasets once data acquisition is complete. In either case, this method of S/N enhancement requires that:

    • The analyte signal must be stable
    • The source of noise is random

    How Ensemble Averaging Works

    • Repeated experiments (scans) are performed on the chemical system in question. The scans are averaged either in real-time or after the data acquisition is complete. A visualization of this process is shown below for five spectra of 8.8 μg/mL 1,1'-ferrocenedimethanol in water.

    scan_averaging.png

    Pros of Ensemble Averaging

    • Ensemble averaging filters out random noise, regardless of the noise frequency
    • Ensemble averaging is effective, even if the original signal has a S/N<1
    • Ensemble averaging is straightforward to implement
    • Improvement in S/N is proportional to:

    \[\sqrt{\#\textrm{ of datasets averaged together}}\]

    Cons of Ensemble Averaging

    • Requirement of a stable signal
    • Ensemble averaging will not work if noise is not random (e.g. 60 Hz electrical noise)

    Example of Ensemble Averaging

    These simulated 5-μV gaussian signals illustrate S/N improvement of ensemble averaging. The bottom dataset represents a S/N of 2 (single dataset), the middle dataset represents a S/N of 8 (average of 16 datasets), and the top dataset represents a S/N of 20 (average of 100 datasets).

    Click here to work on an ensemble averaging exercise.

    ensemble_averaging_example.png


    This page titled Ensemble Averaging is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Contributor.

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