Noise Retrieval from Averaged Sequences

This Demonstration provides visualization of the averaging effect on the amplitude of random noise. It also shows how the original jaggedness can be restored by multiplying the averaged values by the square root of the number of sequences generated. It plots for comparison a chosen original sequence (or all of them together), the average of all the sequences, and the retrieved sequence.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
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DETAILS

Snapshot 1: one hundred sequences () and sequence length of eighty points ()
Snapshot 2: forty-five sequences () and sequence length of eighty points ()
Snapshot 3: ten sequences () and sequence length of eighty points ()
Snapshot 4: fifteen sequences () and sequence length of twenty points ()
Most work on random noise focuses on its elimination or filtration. However, there are situations where one wants to recover noise that has been suppressed. This Demonstration generates a chosen number of random sequences, , each containing a chosen number of points, . It then averages all the sequences, after which it multiplies the averaged values by the square root of the number of sequences, . You can choose whether to plot all the generated sequences together or any individual sequence alone. The averaged sequence in which the noise amplitude is evidently suppressed is plotted next. The third plot displays the averaged sequence after each of its values has been multiplied by . You can see the similarity between the recreated sequence shown in the bottom plot and any of the original sequences displayed in the top plot.
For a new Demonstration, any existing data must first be deleted by clicking on the "clear old" data button and then clicking the "generate new" button. The number of sequences, , and the number of points in each, , are selected with sliders. A checkbox allows you to choose between displaying all the generated sequences together in the top plot or selecting for display any individual sequence by its index number, , using the slider below.
References:
D. Ulbricht, M. D. Normand, M. Peleg, and J. Horowitz, "Assessment of the Crumbliness of Individual Fragile Particulates from That of Their Assemblies," Powder Technology, 81, 1994 pp. 83–91.
D. Ulbricht, M. D. Normand, and M. Peleg, "Creating Typical Jagged Force-Deformation Relationships from the Irregular and Irreproducible Compression Data of Crunchy Foods," Journal of the Science of Food and Agriculture, 67, 1995 pp. 453–459.
D. Robertson. "Noise Averaging." Physics Virtual Library.
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