DEALING WITH MEASUREMENT NOISE

(A gentle introduction to noise filtering)

CONTENTS

The 1st-order Low-pass Filter

The Exponentially Weighted Moving Average filter is identical to the discrete first-order low-pass filter - a commonly available feature in most process computers. The objective of this section is to show their equivalence.

Consider the Laplace transfer function of a first-order low-pass filter, with time constant .

which relates the filtered signal to the measurement . This has the following time domain equivalent:

(Note: this differential equation can also be used to describe the input and the output behaviour of an electrical RC-circuit)

Now, the differential equation can be discretised using the approximation:

where T_s is the interval between each measurement, i.e. the sampling interval. Thus the differential equation representing the first-order low pass filter is converted to:

Simplification and re-arrangement gives:

By letting

  ,

then

which is identical to the Exponentially Weighted Moving Average filter.

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