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Table of Contents General Processing Steps Data Preprocessing Signal and Noise | |
See also: Types of Noise, origin of noise, time averaging, Coefficient of Variation |
Any value obtained by a measurement contains two components: one carries the information of interest, the signal, the other consists of random errors, or noise, that is superimposed on the first component. These random errors are, of course, unwanted because they diminish the accuracy and precision of the measurement.
The term "signal" is sometimes used for the pure, noise-free signal but sometimes also for the noisy "raw" data. The term noise originates from radio engineering, where it describes the unwanted signal that we hear when we do not exactly tune our radio to a radio station. Noise may be present in many different types of signals. Click on the image on the left see a few examples.
Noise free data can never be realized in practice since some types of noise are the result of thermodynamic and quantum effects that cannot be avoided during a measurement. But measurements produced from non-electronic devices are also contaminated with random errors.
There are two methods of calculating the SNR. The first is mainly applied to constant signals and defines the SNR as the ratio of the mean and the standard deviation of the measured signal.
SNR = / s
When the signal is a transient one, i.e. its intensity varies with time, then we use the ratio of the maximum and the standard deviation of the measured signal.
SNR = x_{max} / s
The signal to noise ratio can be improved by repeating a measurement several times and summing up the results. The SNR improves with the square root of the number of repetitions (see section on time averaging for more details).
Last Update: 2006-Jän-18