Imagine filming a helicopter rotor with a 24 fps camera. Suddenly the rotor appears to stand still or spin backwards – although it physically rotates forward. The same effect happens when sampling an audio signal too slowly. It is called aliasing and is the most common cause of unusable acoustic measurements.
The Shannon-Nyquist theorem
The sampling rate fs must be at least twice the highest frequency fmax present in the signal.
The Nyquist frequency
Anything above fNyq gets mirrored in the spectrum – a component at fNyq + Δ appears as a ghost at fNyq − Δ.
Aliasing visualised
Sample a 7 kHz sinusoid at fs = 10 kHz: Nyquist is 5 kHz, the 7 kHz component aliases to:
Without prior knowledge there is no way to tell whether 3 kHz is real or an alias. Hence every clean measurement requires an anti-aliasing low-pass filter before the A/D converter.
Anti-aliasing filters
Real-world filters (Butterworth, Elliptic) have finite roll-off and need 10–20 % margin. Rule of thumb:
Practical recommendations
| Application | Highest relevant frequency | Recommended sample rate |
|---|---|---|
| Comfort acoustics (human hearing) | 20 kHz | 48 or 51.2 kHz |
| Standard NVH (motors, pumps) | 20 kHz | 51.2 kHz |
| E-drives, high switching freq. | 40 kHz | 96 or 102.4 kHz |
| Resonance analysis steel | 30 kHz | 96 kHz |
| Resonance analysis ceramics | 100 kHz | 250 kHz |
| Acoustic emission | 500 kHz | 1 MHz and above |
Oversampling pays – but not infinitely
A higher sample rate yields more data points per second. It does not improve frequency resolution (which depends on frame length), but it eases anti-aliasing filter design. The price: more data, more compute, larger memory footprint for FFT.
What to remember
- Always choose sample rate ≥ 2.5 × highest relevant frequency.
- Analog anti-aliasing filter is not optional – it is physically required.
- Aliasing is invisible in the spectrum after the fact. Prevent it or you inspect the wrong signal.
