Determine the minimum sampling frequency based on signal bandwidth.
Hz
kHz
MHz
GHz
Standard engineering practice adds a buffer (e.g., 10-20%) for anti-aliasing filters.
Minimum Nyquist Rate (Theoretical)
–
Exactly 2 × Bandwidth
Recommended Practical Rate
–
Includes buffer for filter roll-off
Sampling Interval (Period)
–
Time between samples (1/fs)
function calculateNyquist() {
// 1. Get input values
var bwValue = document.getElementById('bandwidthInput').value;
var unitMultiplier = document.getElementById('unitInput').value;
var bufferPercent = document.getElementById('oversamplingInput').value;
var resultsDiv = document.getElementById('resultsArea');
// 2. Validation
if (bwValue === "" || isNaN(bwValue) || bwValue < 0) {
alert("Please enter a valid positive number for Bandwidth.");
resultsDiv.style.display = "none";
return;
}
if (bufferPercent === "" || isNaN(bufferPercent) || bufferPercent = 2 * B
var nyquistHz = bandwidthHz * 2;
// Practical Rate: Nyquist * (1 + buffer/100)
var practicalHz = nyquistHz * (1 + (parseFloat(bufferPercent) / 100));
// Period: T = 1 / fs (using practical rate)
var periodSeconds = 0;
if (practicalHz > 0) {
periodSeconds = 1 / practicalHz;
}
// 4. Formatting Helpers
function formatFreq(hz) {
if (hz >= 1000000000) return (hz / 1000000000).toFixed(3) + " GHz";
if (hz >= 1000000) return (hz / 1000000).toFixed(3) + " MHz";
if (hz >= 1000) return (hz / 1000).toFixed(3) + " kHz";
return hz.toFixed(2) + " Hz";
}
function formatTime(sec) {
if (sec === 0) return "Infinite";
if (sec < 0.000001) return (sec * 1000000000).toFixed(2) + " ns";
if (sec < 0.001) return (sec * 1000000).toFixed(2) + " µs";
if (sec < 1) return (sec * 1000).toFixed(2) + " ms";
return sec.toFixed(4) + " s";
}
// 5. Update UI
document.getElementById('nyquistResult').innerHTML = formatFreq(nyquistHz);
document.getElementById('practicalResult').innerHTML = formatFreq(practicalHz);
document.getElementById('intervalResult').innerHTML = formatTime(periodSeconds);
resultsDiv.style.display = "block";
}
How to Calculate Sampling Rate from Bandwidth
In digital signal processing (DSP) and telecommunications, converting an analog signal into a digital stream requires selecting an appropriate sampling rate. If the sampling rate is too low, the signal cannot be reconstructed correctly due to a phenomenon called aliasing.
The Nyquist-Shannon Sampling Theorem
The fundamental rule governing this conversion is the Nyquist-Shannon Sampling Theorem. It states that to perfectly reconstruct a continuous-time signal from its digital samples, the sampling frequency ($f_s$) must be greater than twice the highest frequency component (bandwidth, $B$) of the signal.
fs > 2 × B
B (Bandwidth): The highest frequency present in the analog signal (usually measured in Hertz).
fs (Sampling Rate): The number of samples taken per second.
Nyquist Rate: The absolute minimum sampling rate required ($2B$).
Why Do We Need a Buffer? (Practical Sampling)
While the math says $2 \times B$ is sufficient, real-world engineering requires a higher rate. This is because analog "anti-aliasing" filters are not perfect "brick walls." They need a transition band to attenuate frequencies above the bandwidth.
For example, human hearing ranges up to 20 kHz. According to Nyquist, we need 40 kHz. However, CD audio uses 44.1 kHz. The extra 4.1 kHz provides a buffer (oversampling) to allow for practical filter design without distorting the audible signal.
Step-by-Step Calculation
Identify the Bandwidth: Determine the highest frequency relevant to your signal. For a voice call, this might be 4 kHz.
Apply Nyquist Formula: Multiply the bandwidth by 2. ($4 \text{ kHz} \times 2 = 8 \text{ kHz}$).
Add Engineering Buffer: Add 10% to 20% to account for hardware limitations. ($8 \text{ kHz} \times 1.1 = 8.8 \text{ kHz}$).
Common Bandwidths and Sampling Rates
Application
Bandwidth (Max Freq)
Min. Nyquist Rate
Standard Used Rate
Telephone (Voice)
~3.4 kHz
6.8 kHz
8 kHz
FM Radio
15 kHz
30 kHz
32 kHz or 44.1 kHz
CD Audio
20 kHz
40 kHz
44.1 kHz
Professional Audio
24 kHz
48 kHz
48 kHz / 96 kHz
FAQ: Sampling Rate and Bandwidth
What happens if the sampling rate is too low?
If $f_s < 2B$, aliasing occurs. High-frequency components "fold over" into the low-frequency spectrum, creating noise and distortion that cannot be removed later. This makes the original signal unrecoverable.
Is a higher sampling rate always better?
Not necessarily. While higher rates (oversampling) simplify filter design and improve signal-to-noise ratio (SNR), they also increase data storage requirements and processing power. The goal is to find the optimal rate that satisfies the Nyquist criterion with a reasonable buffer.
What is the Nyquist Frequency vs. Nyquist Rate?
Nyquist Rate is $2 \times B$ (the property of the signal). Nyquist Frequency is $f_s / 2$ (the property of the sampler, representing the maximum frequency the system can capture).