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Noise averaging

This applet was written to support an Instumentation course. It can be used to demonstrate how multiple samples of an input stimuli can be averaged to reduce the signal to noise ratio.
* Noise is defined as a random and unwanted component that accompanies a desired signal. It manifests itself in many areas of physics, and a variety of techniques are available to help experimenters increase the signal to noise ratio (SNR) present in their work. Wanted signal recovery is possible due to the fact there is coherence within the wanted signal that distinguishes it from the ever changing background noise. This leads us on to the idea of noise averaging. The concept behind the method is simply to capture and store the system response signal each time it is sampled. The nature of this signal should be such that the wanted component is identical each time it is sampled; the noise present in the total signal however will be random each time. By collecting a number of signals and averaging them it is possible to abstract the generated signal from the background noise even when you can scarecely see it. This is due to the fact that if N signals are gathered, the desired signal will be N times larger. The noise however will only increase by a factor of root N. Hence the signal to noise ratio increases as root N.

* In the applet, the noisy signal can be contolled using the first two panels. Below the panels is the signal that we want to extract, which can be taken to be the response of a system to a stimulus, e.g. in an NMR experiment. Its wavelength can be changed by the slider. The second panel allows the user to set the SNR, which defaults as 1:1. The allowed range is 0.1 to 10. Use the RETURN key after entering a new number in the box.

* Below is shown the actual response of the system as signal plus noise.

* Finally, below that is the effect of averaging N signals each of which has randomly different noise component. The value of 'N' is shown on the top right.

* The animation is run using the buttons on the third control panel.

* Try decreasing the SNR to low values (down to 0.1), and observe how long it takes for a 'clean' signal to form.

Applet produced and written by Douglas Robertson, from an initial idea by Dr Iain Mackenzie.


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