Nyquist Rate
Sample at least twice the highest frequency to avoid aliasing.
Formula
Variables
Example
Audio to 20 kHz needs f_s ≥ 40 kHz (CD uses 44.1 kHz)
How it works
When a continuous signal is sampled, each sample only records the signal at discrete instants, so the sampling rate must be high enough to capture the fastest oscillations present. If the sampling rate is at least twice the highest frequency component, those components can be distinguished unambiguously in the sampled data; if not, higher frequencies can masquerade as lower ones, which is aliasing. This condition comes from the sampling theorem and represents the minimum rate needed for perfect reconstruction in an ideal system.
When to use it
Use this when designing or checking ADCs, digital audio/video systems, sensors, or any measurement pipeline that converts analog signals into samples. It is especially important whenever you know the highest frequency content of the signal and need to choose a safe sampling rate.
Worked example, step by step
A vibration sensor measures machinery motion up to 3.2 kHz. Given: f_max = 3.2 kHz Nyquist condition: f_s ≥ 2 f_max Substitute: f_s ≥ 2 × 3.2 kHz Compute: f_s ≥ 6.4 kHz So the sampling rate must be at least 6.4 kHz to avoid aliasing. In practice, you would pick a higher standard rate, such as 8 kHz or more, to leave design margin.
Common mistakes to avoid
- Using the highest frequency of the sampled data after aliasing instead of the true source frequency
- Choosing a sampling rate equal to f_max rather than at least 2 × f_max
- Ignoring extra bandwidth from filters, noise, or harmonics and sampling too close to the limit
Did You Know?
CD audio's 44.1 kHz rate leaves headroom above the 40 kHz Nyquist minimum for gentle anti-alias filtering.
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