Simcenter Testing Solutions Data Acquisition: Anti-Aliasing Filters

Direct YouTube link: https://youtu.be/aDS-Au5m0E8

 

*** Check out the webinars Digital Data Acquisition and Digital Signal Processing ***

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

Aliasing occurs when a dynamic event is not sampled fast enough to truly capture what is happening.  For example, in movies the wheels of a vehicle sometimes appear to being going backward, even though the vehicle is moving forward.  This is because the frame rate of the movie camera was not fast enough.  

This article has the following sections:
   1. What is Aliasing
   2. Preventing Aliasing with Filters
   3. Simcenter SCADAS Anti-Aliasing Filter
   4. Simcenter Testlab: Span versus Bandwidth
   5. Conclusion

1. What is 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.

Figure 1: Aliasing is caused when the digital sampling rate is not adequate to capture the fluctuations in an analog signal, and results in the wrong frequency being identified. The red sine wave is the original signal. The blue dots represent how often the signal is being sampled. The blue line is how the signal will appear at the wrong frequency due to the low sampling rate. 

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): Absolute maximum frequency (or bandwidth) content that can be digitized, and eventually reconstructed back, if sample rate is at least twice as Nyquist rate (Nyquist-Shannon theorem). 

To properly sample all the desired frequency content of an incoming signal, 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. 

When 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.

In Figure 2a, a sine wave with inadequate sampling (violating the Nyquist theroem) is shown.  The frequency is not identified properly.

In Figure 2b, a sine wave with adequate sampling shows the proper frequency.

Figure 2: fs represents the sampling frequency, fsin¬e represents the frequency of the sine wave. a) When sampling at the same frequency as the incoming signal, the observed frequency is zero Hertz. b) When sampling at twice the frequency of the sine wave, the observed frequency is fsine, the true frequency of the sine wave.

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 as shown in Figure 3.

Figure 3: Aliasing causes frequency above the bandwidth to be mirrored across the bandwidth.

Here, the bandwidth is 1000 Hertz. The actual frequency component in the signal is at 1300 Hertz. The frequency is 300Hz over the bandwidth. It will be mirrored 300 Hertz below the bandwidth at 700 Hertz.

A table of aliased frequencies (observed) versus actual frequencies is shown in Figure 4 for 100 Hertz bandwidth measurement performed without aliasing considerations.

Figure 4: This table shows the actual frequency being acquired by the system vs the observed frequency after sampling. For all frequencies being acquired, the bandwidth is 100Hz.

Imagine trying to measure a signal that has a 125 Hertz sine wave and the measurement system identifies it as 75 Hertz!

2. Preventing Aliasing with Filters

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). This makes it so a 125 Hertz sine wave does not show up as 75 Hertz.

The ideal anti-aliasing filter would be shaped like a “brick wall”, completely attenuating all signals beyond the specified bandwidth (Figure 5).

Figure 5: The ideal anti-aliasing filter would be shaped like a wall: cutting off all frequencies beyond the specified bandwidth (fs/2).

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 as shown in Figure 6.

Figure 6: The anti-aliasing filter has a -3dB roll off point at the bandwidth.

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.

Equation 1: Span is 80% of the bandwidth

If the bandwidth was set at 1000Hz, the span would be 800Hz. Figure 7 shows the span without alias effects and the bandwidth with alias effects.

Figure 7: The spectral content is being mirrored about the bandwidth. All mirrored content is between 80% of the bandwidth and the full bandwidth. The alias free frequency range is from 0Hz to 80% of the bandwidth, also known as the span.

The Simcenter 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.

3. Simcenter SCADAS Anti-Aliasing Filter

The anti-aliasing protection in a Simcenter SCADAS consists of at least two filters (one analog, one digital) as shown in Figure 8 below.
 

Figure 8: The anti-aliasing filters of a Simcenter SCADAS input card have an analog filter and a digital filter.  The analog filter operates at the full bandwidth of the card while the digital filter is applied while downsampling to the desired measurement bandwidth.

When an analog signal enters a Simcenter SCADAS, an analog anti-aliasing filter is applied to the incoming signal with a cutoff at the full bandwidth of the module.  The filter has an attenuation on the order of 150 dB per octave to prevent aliasing during the analog to digital conversion process.

After the signal is digitized, a second digital anti-aliasing filter is applied.  This is applied to the digital signal during downsampling from the full bandwidth to the desired measurement bandwidth.

The anti-aliasing filters include both passive and active components.  Operational amplifiers are used in the design of the filter and are part of the active components. Passive components include resistors, inductors, and capacitors. The passive components are used to protect the active components at high frequency and at high input levels.

The anti-aliasing filter on a Simcenter SCADAS can never be turned off. Depending on the input card, additional filters can be applied to prevent the Gibbs phenomenon. 

4. Simcenter Testlab: Span versus Bandwidth

In Simcenter Testlab 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 Simcenter Testlab as the span instead of bandwidth. 

Direct YouTube link: https://youtu.be/bZnv4JOxs0U

This is done in the Simcenter Testlab main menu under "Tools -> Options -> General tab -> Frequency: Span/Bandwidth/Sampling Rate".

5. Conclusion

• Aliasing is properly prevented by an anti-aliasing filter. 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 required.
• The useful measurement bandwidth (span) will always be smaller than the Nyquist rate. An anti-aliasing filter always needs roll off space between passband and stopband frequencies, so that signal gets minimally and maximally attenuated at passband and stopband respectively. The alias-free portion of the bandwidth is called the span. The span is the approximately 80% of the bandwidth (on many acquisition systems).Always set the bandwidth 20% higher than the highest frequency of interest to avoid aliasing.

Questions? Email charles.rice@siemens.com or contact Siemens Support Center.

Related Digital Signal Processing Links:

• Index of Testing Knowledge Articles
• NVH Testing and Data Acquisition
• Digital Signal Processing: Sampling Rates, Bandwidth, Spectral Lines, and more...
• Gain, Range, Quantization
• Acquisition Filters and Overshoot
• Overloads
• Averaging Types: What's the difference?
• Overlap: What, Why and How to use it
• What is Fourier Transform?
• Time-Frequency Analysis: Wavelets
• Spectrum versus Autopower
• Autopower Function...Demystified!
• Power Spectral Density
• Shock Response Spectrum (SRS)
• Windows and Leakage
• Window Types
• Window correction factors
• Exponential Window Correction Factors
• RMS Calculations
• The Gibbs Phenomenon
• Introduction to Filters: FIR and IIR
• Digital Data Acquisition and Signal Processing Seminar
• Digital Signal Processing YouTube Playlist

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• Simcenter SCADAS XS: Everything you need to know!
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