DEALING WITH MEASUREMENT NOISE

(A gentle introduction to noise filtering)

CONTENTS

Averaging Filter

Simple averaging can be used to reduce the effects of noise. Suppose we have n measurements of a variable x. The standard deviation of this measured variable can be estimated by:

where is the mean or average of the n measurements calculated as:

The magnitude of s is clearly dependent on the measurements, , which in practice is bounded, that is it has lower and upper limits. However, s is also dependent on the number of measurements made, i.e. the number n. Thus for bounded values of , it can be deduced that the larger n is, the smaller s becomes. In other words, given a noisy but bounded measurement sequence, we can take a large number of readings of the variable and use its average to give a better estimate of its true value (provided there is no systematic error or bias in the measurements). This is actually standard procedure in experimental work, where a number of readings are taken at a sampling instant and the average of these readings used as the measurement.

Although it is simple to calculate averages using the formula above, for online applications, it is inefficient both in terms of storage and computational requirements. This is because we need to:

• store n data values
• perform n additions and 1 division

Given that computer storage and high speed microprocessors are very cheap nowadays, this may not seem to be a problem. However, the load on a process computer can become quite significant when you consider the fact that hundreds, and perhaps even thousands, of measurements are made on a typical process plant. We therefore need to look at more efficient ways of calculating averages.

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