Formula & Calculator
Nyquist Sampling Rate
States the minimum sampling rate required to reconstruct a band-limited signal without aliasing.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| f_s | Sampling frequency | Hz |
| f_max | Maximum signal frequency | Hz |
What it means
The Nyquist sampling theorem states that to accurately reconstruct a band‑limited signal, it must be sampled at a frequency at least twice the highest frequency component present. The minimum sampling rate is f_s ≥ 2·f_max. If sampling below this rate, aliasing occurs, where high‑frequency components fold into lower frequencies, distorting the signal. This theorem is the basis for digital signal processing, analog‑to‑digital conversion, and audio/video compression. In practice, sampling rates are chosen with a margin above the Nyquist rate (e.g., 44.1kHz for audio with a 20kHz bandwidth). Example: An audio signal with a maximum frequency of 20kHz must be sampled at f_s ≥ 40kHz. The standard CD sampling rate is 44.1kHz, which satisfies Nyquist and provides a margin.
Worked example
Nyquist Sampling – Practical Example
Real‑World| Parameter | Value |
|---|---|
| fmax | 20 kHz |
| Formula | fs ≥ 2·fmax |
Common mistakes
Watch unit consistency and the assumptions behind the formula; misapplying it outside its valid conditions is the most frequent error.Applications
Nyquist sampling rate f_s ≥ 2·f_max ensures that a signal can be reconstructed without aliasing. This is a cornerstone of digital signal processing and data acquisition. Engineers use it to set the sampling frequency of ADCs, to design anti‑aliasing filters, and to avoid distortion in digital systems. By adhering to the Nyquist criterion, they can faithfully capture signals. This principle applies to audio, video, sensor data, and many other applications. Understanding the Nyquist rate is essential for any engineer working with sampled data.
- ADC sampling frequency selection for signal acquisition
- Anti‑aliasing filter design for data conversion
- Digital audio and video processing
- Sensor data acquisition and signal processing
- Educational understanding of sampling theory