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Siemens Experimenter

09-29-2016
04:08 PM

When converting signals from their true analog form into digital form, frequency errors can be induced due to “aliasing”.

Aliasing is an effect that causes distortion in the spectrum of a sampled signal due to the sampling rate being too low to capture the frequency content properly. Aliasing causes high frequency data to appear at a lower frequency than it actually is (see Figure 1 below): thus assuming a “false identity” frequency or “alias” frequency.

Some essential terms to know when talking about aliasing:

**Sampling frequency**(Hz): The number of samples per second being acquired of an incoming frequency. The sampling frequency is two times the bandwidth.

**Bandwidth**(Hz): The frequency range over which measurements will be taken. Bandwidth is defined as half of the sampling frequency.

**Span**(Hz): The frequency range over which measurements will be taken and not be effected by the anti-aliasing low-pass filters (i.e.*the alias-free region of the bandwidth*). The span is 80% of the bandwidth.

**Nyquist rate**(Hz): Minimum frequency at which a signal can be sampled without introducing frequency errors. The Nyquist rate is twice the highest frequency of interest in the sample.

To properly sample all the desired frequency content of an incoming signal, and thereby avoid aliasing, one must sample at (or above) the *Nyquist rate*. In data acquisition, the sampling frequency is twice as high as the specified bandwidth. So, all frequency content below the specified bandwidth will be sampled at a rate sufficient to accurately capture the frequency content. However, if the incoming signal contains frequency content above the specified bandwidth, the sampling frequency (2x bandwidth) will violate the Nyquist theorem for this higher frequency content.

When the Nyquist theorem is violated, spectral content above the bandwidth is mirrored about the bandwidth frequency. This means that frequency content X Hz above the bandwidth will then appear X Hz below the bandwidth. Watch the video at the top of this article to see mirroring in action.

Thus, higher frequency content appears to be at a lower frequency, or an “alias” frequency.

**Preventing Aliasing**

An anti-aliasing filter is a low-pass filter that removes spectral content that violates the Nyquist criteria (aka spectral content above the specified bandwidth). The ideal anti-aliasing filter would be shaped like a “brick wall”, completely attenuating all signals beyond the specified bandwidth (see Figure 5).

In the real world, it is impossible to have this “wall shaped” filter. Instead, a very sharp analog filter is used that has a -3dB roll off at the bandwidth and attenuates all frequencies 20% beyond the bandwidth to zero.

This is why the “trustable”, alias-free region of the spectrum is from zero Hz to 80% of the bandwidth. This alias-free range is called the frequency span.

If the bandwidth was set at 1000Hz, the span would be 800Hz.

The LMS SCADAS hardware has an anti-aliasing filter built into it. The video at the top of this article demonstrates how this anti-aliasing filter works.

TIP: Remember to set the bandwidth at least 20% higher than the highest frequency of interest.

In Test.Lab, it is possible to specify the span instead of the bandwidth. This way, you can be sure all data up to that frequency value will be alias free. See Video 2 below for instructions on how to set the default view in LMS Test.Lab as the span instead of bandwidth (Tools -> Options -> General tab -> Frequency: Span/Bandwidth/Sampling Rate).

**Conclusion:**

Aliasing can cause spectral content to be mirrored about the bandwidth thus causing false representation of the frequency content. To prevent this an anti-aliasing filter is implemented. The alias-free portion of the bandwidth is called the span. The span is the first 80% of the bandwidth. Remember, always set your bandwidth 20% higher than the highest frequency of interest to avoid aliasing.

**Related Digital Signal Processing Links: **

- Digital Signal Processing: Sampling Rates, Bandwidth, Spectral Lines, and more...
- Gain, Range, Quantization
- Aliasing
- Overloads
- Averaging Types: What's the difference?
- Spectrum versus Autopower
- Autopower Function...Demystified!
- Power Spectral Density
- Windows and Leakage
- Window Types
- Window correction factors
- RMS Calculations
- The Gibbs Phenomenon

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