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Sampling, Aliasing, and Analog Anti-Alias Filtering

Filtering topics:

 

This page describes the problem of aliasing that arises when analog data is sampled for filtering in a digital system. This is part of the section on
Filtering that is part of
A Guide to Fault Detection and Diagnosis..

The aliasing problem that arises from sampling

When data is sampled at discrete points in time, faster sampling periods make it possible to accurately see higher frequences and faster changes in signals. For a sine wave of with a period P, the signal must be sampled at least twice in the time period P to even be able to theoretically reconstruct the original signal, even knowing that no higher frequencies are present (Shannon’s sampling theorem). From a practical standpoint, not using an ideal filter designed for this reconstruction (and not knowing what frequencies are really present), it is best to sample at least 3 to 4 times within the period of the highest frequency signal of interest.

 If the sampling rate is inadequate, aliasing will make the high frequencies appear as if they were lower frequencies. The noise at those higher frequencies is not eliminated -- it is just converted to lower frequency noise. This is best illustrated by plotting the sampled data and interpolating the points between the samples. The signal in blue below represents interpolated values from the points sampled at too low a rate. (Those points are sampled at equal time intervals - it is only an optical illusion that they aren’t!)

 

Aliasing Example

 

Analog filtering to reduce aliasing

To reduce the effects of aliasing when sampling analog signals, analog filtering must first be used to reduce the higher frequencies. Data sampled for process control use will typically have a first order analog RC (resistor-capacitor) filter. For a first order analog filter, a filter time constant at least 3 times the sample interval is often appropriate for reducing aliasing in a diagnostic system. The required analog filtering is called an anti-aliasing filter.

Supervisory systems like diagnostics are prone to aliasing problems

Diagnostic systems typically work from data sampled at a lower rate than that used for process control. As a result, aliasing is a concern. This is especially an issue in monitoring systems for the process industries, because of the prevalence of control loops that cause cycling. Be sure that adequate filtering is present before sampling for diagnostic use to significantly reduce the effects of these frequencies, except for cases where high frequency noise is a symptom of a fault of interest. For an exponential filter in the more rapidly scanned process control system, to minimize aliasing in the more slowly scanned diagnostic system, a filter time constant equal to several times the diagnostic sampling time could be appropriate. The diagnostic system should have a sample time less than 1/3 or 1/4 the period of noise frequencies related to controller cycling.

Copyright 2010 - 2013, Greg Stanley

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