Nyquist Sampling Rate
Minimum sampling rate to capture a signal without aliasing.
Formula
Variables
Example
CD audio: 44.1 kHz
How it works
A continuous signal must be sampled fast enough that consecutive samples still capture its fastest changes; otherwise different waveforms can look identical after sampling. The Nyquist condition says the sampling rate must be at least twice the highest frequency present, because one cycle of the highest-frequency component needs at least two samples to be distinguishable. If you sample below this threshold, high-frequency content can masquerade as lower-frequency content, creating aliasing artifacts that cannot be undone after the fact.
When to use it
Use this when designing or checking digital acquisition systems such as audio, sensors, oscilloscopes, or image/video capture pipelines. It is also essential when deciding whether an anti-aliasing filter is needed before analog-to-digital conversion.
Worked example, step by step
Suppose a vibration sensor must record frequencies up to 8.5 kHz. Step 1: Identify the highest frequency. f_max = 8.5 kHz Step 2: Apply the Nyquist condition. f_s ≥ 2f_max f_s ≥ 2 × 8.5 kHz f_s ≥ 17 kHz Step 3: Interpret the result. The sampling rate must be at least 17 kHz to avoid aliasing. Step 4: Choose a practical rate above the minimum. For example, 20 kHz would satisfy the requirement.
Common mistakes to avoid
- Using the Nyquist rate as the exact recommended rate instead of the minimum; in practice you often need extra margin and a pre-sampling low-pass filter
- Applying the formula to the average frequency of a signal instead of the highest frequency component present
- Thinking that a high sampling rate alone prevents aliasing, even when frequencies above the limit are still allowed into the input
Did You Know?
The Nyquist theorem says you must sample at twice a signal's frequency, why CDs sample audio at 44.1 kHz.
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