Nyquist Sampling Rate
fs_min = 2 × fmax
Quick answer
This calculator solves fs_min = 2 × fmax for Min Sampling Frequency. With Max Signal Frequency 0.22 MHz, the result is 0.44 MHz. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The Nyquist-Shannon sampling theorem states that to perfectly reconstruct a band-limited signal, the sampling rate must be at least twice the highest frequency component in the signal. Sampling below this rate causes aliasing, where high-frequency components fold back into the sampled bandwidth as spurious lower-frequency signals that cannot be removed. This is why audio CDs sample at 44.1 kHz (just over 2 × 20 kHz human hearing limit) and why anti-aliasing filters are placed before ADC inputs to remove frequencies above fs/2.
Variables
- fs_min — Minimum sampling frequency (Hz)
- fmax — Maximum signal frequency (Hz)
Practical Notes
In practice, sample at 2.5-10x the maximum frequency to ease anti-aliasing filter requirements and improve reconstruction quality. Oversampling (sampling much faster than Nyquist) trades speed for resolution and simplifies analog filter design. Sigma-delta ADCs exploit extreme oversampling (64-256x) followed by digital decimation filtering.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| fs | Min Sampling Frequency | kHz | Hz, kHz, MHz, GHz |
| fmax | Max Signal Frequency | kHz | Hz, kHz, MHz, GHz |
Step by step
- 1. What you know: Max Signal Frequency 0.22 MHz
- 2. The relation: fs_min = 2 × fmax
- 3. Substitute: fmax = 0.22 MHz
- 4. Result: Min Sampling Frequency = 0.44 MHz
Worked examples
Minimum range
Given: Max Signal Frequency 0.22 kHz
Result: Min Sampling Frequency = 0.44 kHz
Low range
Given: Max Signal Frequency 2.2 kHz
Result: Min Sampling Frequency = 4.4 kHz
Typical
Given: Max Signal Frequency 0.22 MHz
Result: Min Sampling Frequency = 0.44 MHz
High range
Given: Max Signal Frequency 1.1 MHz
Result: Min Sampling Frequency = 2.2 MHz
Maximum range
Given: Max Signal Frequency 11 MHz
Result: Min Sampling Frequency = 22 MHz
Solving for each variable
Solve for Min Sampling Frequency
Max Signal Frequency 0.22 kHz → 0.44 kHz
Solve for Max Signal Frequency
Min Sampling Frequency 100 Hz → 50 Hz
How Min Sampling Frequency changes with Max Signal Frequency
| Max Signal Frequency (input) | Min Sampling Frequency (result) |
|---|---|
| 48.4 kHz | 96.8 kHz |
| 121 kHz | 0.242 MHz |
| 0.242 MHz | 0.484 MHz |
| 0.363 MHz | 0.726 MHz |
| 0.484 MHz | 0.968 MHz |
| 0.726 MHz | 1.452 MHz |
| 0.968 MHz | 1.936 MHz |
| 1.936 MHz | 3.872 MHz |
| 3.388 MHz | 6.776 MHz |
| 4.84 MHz | 9.68 MHz |
The same result in other units
| Unit | Value |
|---|---|
| Hz | 440000 |
| kHz | 440 |
| MHz | 0.44 |
| GHz | 0.00044 |
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<p><a href="https://vbatpower.com/formulas/nyquist/">Nyquist Sampling Rate</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Nyquist Sampling Rate?
Use fs_min = 2 × fmax. With Max Signal Frequency 0.22 MHz, Min Sampling Frequency works out to 0.44 MHz.
What is the formula for Nyquist Sampling Rate?
The formula is fs_min = 2 × fmax. The Nyquist-Shannon sampling theorem states that to perfectly reconstruct a band-limited signal, the sampling rate must be at least twice the highest frequency component in the signal.
How do you find Max Signal Frequency when you know the other values?
Rearrange for Max Signal Frequency: with Min Sampling Frequency 100 Hz, Max Signal Frequency is 50 Hz.
What units does Nyquist Sampling Rate use?
Min Sampling Frequency is shown in Hz, kHz, MHz, GHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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