Aliasing in Digital Signal Processing: The Hidden Enemy
Ever wondered why your vibration measurements don’t match reality? Or why that expensive accelerometer seems to be lying to you? The culprit might be aliasing—a fundamental phenomenon that can completely destroy the validity of your data. Let’s dive deep into this critical concept that every engineer working with digital signals must understand.
What is Aliasing? The 60-Second Explanation
Imagine you’re trying to film a rotor blades with your smartphone camera. Sometimes the blades appear to be moving slowly or even backwards. This visual illusion is exactly what happens to your digital signals when aliasing occurs, see the video below.
Aliasing is the phenomenon where high-frequency signals masquerade as low-frequency signals after digital sampling. Once this happens, you cannot tell the difference between the real low-frequency signal and the imposter high-frequency signal that’s been “aliased” down.
The Mathematics Behind the Madness
The core of aliasing lies in the Nyquist-Shannon sampling theorem, which states that to accurately reconstruct a signal, you must sample at least twice the highest frequency component present in the signal.
Key formulas to remember:
– Nyquist frequency: \[f_{nyquist} = \frac{f_{sample}}{2} \tag{1}\]
– Aliasing formula: \[f_{aliased} = |n \times f_{sample} \pm f_{original}| \tag{2}\]
Where n is any integer (0, 1, 2, …), and $f_{original}$ is the frequency of the signal being aliased.
Aliasing in Vibration Signal Measurement
⚠️ Note: Aliasing Cannot Be Fixed After Sampling!
Once aliasing occurs, you cannot distinguish between the true signal and the aliased signal. This demonstration shows why proper analog filtering before digitization is absolutely essential.
Simple Example
1. Continuous Analog Signals (Before Sampling)
What you see: Two clearly different sinusoidal signals - one at 20 Hz and one at 180 Hz.
Note: The 180 Hz signal is shown with a vertical offset for visual clarity.
2. Digital Sampling Points
What happens: When sampled at 200 Hz, we only capture 10 points per 20 Hz cycle, but only 1.11 points per 180 Hz cycle!
Note: The 180 Hz signal is shown with a vertical offset for visual clarity.
3. Reconstructed Digital Signals
🔥 Note: Both Signals Look Identical!
After sampling, both the 20 Hz and 180 Hz signals appear as identical 20 Hz signals. There is NO way to tell them apart from the digital data alone.
Note: The aliased 180 Hz signal is shown with a vertical offset for visual clarity.
4. Frequency Domain Analysis (FFT)
FFT Results: Both signals show a peak at 20 Hz. The 180 Hz energy has been "folded" down to 20 Hz.
5. The Solution: Anti-Aliasing Filter
✅ Prevention Strategy:
The solution is to use an analog low-pass filter, known as an anti-aliasing filter, before the signal is digitized.
- For our example with a 100 Hz Nyquist frequency, we must use a filter with a cutoff frequency below 100 Hz.
- This filter will pass the desired 20 Hz signal with little to no attenuation.
- It will significantly attenuate the 180 Hz signal, removing it before it has a chance to be sampled and cause aliasing.
• Nyquist-Shannon Theorem: Sample Rate > 2 × Maximum Frequency of Interest
• Anti-Aliasing Filter: The filter's cutoff frequency should be set below the Nyquist frequency (Sample Rate / 2) to effectively remove unwanted higher frequencies.
Aliasing in Vibration Signal Measurement
⚠️ Note: Aliasing Cannot Be Fixed After Sampling!
Once aliasing occurs, you cannot distinguish between the true signal and the aliased signal. This demonstration shows why proper analog filtering before digitization is absolutely essential.
Simple Example
| Parameter | Value | Notes |
|---|---|---|
| Signal (1) | 20 Hz sine wave | Within measurement bandwidth |
| Signal (2) | 180 Hz sine wave | Above Nyquist frequency |
| Sample Rate | 200 Hz | Chosen sample rate |
| Nyquist Frequency | 100 Hz | Sample rate ÷ 2 |
| Aliased Frequency | 20 Hz | |200 Hz - 180 Hz| = 20 Hz |
1. Continuous Analog Signals (Before Sampling)
What you see: Two clearly different sinusoidal signals - one at 20 Hz and one at 180 Hz.
Note: The 180 Hz signal is shown with a vertical offset for visual clarity.
2. Digital Sampling Points
What happens: When sampled at 200 Hz, we only capture 10 points per 20 Hz cycle, but only 1.11 points per 180 Hz cycle!
Note: The 180 Hz signal is shown with a vertical offset for visual clarity.
3. Reconstructed Digital Signals
🔥 Note: Both Signals Look Identical!
After sampling, both the 20 Hz and 180 Hz signals appear as identical 20 Hz signals. There is NO way to tell them apart from the digital data alone.
Note: The aliased 180 Hz signal is shown with a vertical offset for visual clarity.
4. Frequency Domain Analysis (FFT)
FFT Results: Both signals show a peak at 20 Hz. The 180 Hz energy has been "folded" down to 20 Hz.
5. The Solution: Anti-Aliasing Filter
✅ Prevention Strategy:
The solution is to use an analog low-pass filter, known as an anti-aliasing filter, before the signal is digitized.
- For our example with a 100 Hz Nyquist frequency, we must use a filter with a cutoff frequency below 100 Hz.
- This filter will pass the desired 20 Hz signal with little to no attenuation.
- It will significantly attenuate the 180 Hz signal, removing it before it has a chance to be sampled and cause aliasing.
• Nyquist-Shannon Theorem: Sample Rate > 2 × Maximum Frequency of Interest
• Anti-Aliasing Filter: The filter's cutoff frequency should be set below the Nyquist frequency (Sample Rate / 2) to effectively remove unwanted higher frequencies.
References:
- Youtube videos about aliasing by Tom Irvine.
- Shannon, C.E. (1949). “Communication in the Presence of Noise.” Proceedings of the IRE, 37(1), 10-21. – The foundational paper establishing the sampling theorem.
- Nyquist, H. (1928). “Certain Topics in Telegraph Transmission Theory.” Transactions of the AIEE, 47(2), 617-644. – Early work introducing the concept of the Nyquist rate.
- Bendat, J.S. & Piersol, A.G. (2010). Random Data: Analysis and Measurement Procedures (4th ed.). John Wiley & Sons. – Comprehensive coverage of aliasing in vibration measurement.
- Randall, R.B. (2011). Vibration-based Condition Monitoring: Industrial, Automotive and Aerospace Applications
I am a senior CAE and Automation Engineer at Scania with over 7 years of hands-on experience in Finite Element Analysis (FEA). My daily work involves advanced simulations focusing on strength and durability analysis, helping design more reliable and efficient products.
Before joining Scania, I conducted research at KTH Royal Institute of Technology, where I focused on the additive manufacturing of heat exchangers. My work has been recognized internationally and published in peer-reviewed journals. You can find my publications on Google Scholar.
I am a senior CAE and Automation Engineer at Scania with over 7 years of hands-on experience in Finite Element Analysis (FEA). My daily work involves advanced simulations focusing on strength and durability analysis, helping design more reliable and efficient products.
Before joining Scania, I conducted research at KTH Royal Institute of Technology, where I focused on the additive manufacturing of heat exchangers. My work has been recognized internationally and published in peer-reviewed journals. You can find my publications on Google Scholar.