Nyquist Sampling Rate Calculator

Nyquist Sampling Rate Calculator

Hz kHz MHz GHz

Calculation Results

Minimum Nyquist Sampling Rate ($f_s$): –

Nyquist Frequency ($f_n$): –

Nyquist Interval ($T_s$): –

function calculateNyquist() { var fMaxVal = parseFloat(document.getElementById('maxFreq').value); var unitMultiplier = parseFloat(document.getElementById('freqUnit').value); if (isNaN(fMaxVal) || fMaxVal = 1e9) return (hz / 1e9).toFixed(4) + " GHz"; if (hz >= 1e6) return (hz / 1e6).toFixed(4) + " MHz"; if (hz >= 1e3) return (hz / 1e3).toFixed(4) + " kHz"; return hz.toFixed(2) + " Hz"; } function formatTime(sec) { if (sec < 1e-6) return (sec * 1e9).toFixed(4) + " ns"; if (sec < 1e-3) return (sec * 1e6).toFixed(4) + " µs"; if (sec < 1) return (sec * 1e3).toFixed(4) + " ms"; return sec.toFixed(6) + " s"; }

Understanding the Nyquist-Shannon Sampling Theorem

The Nyquist Sampling Rate Calculator is an essential tool for engineers and students working in digital signal processing (DSP), telecommunications, and audio engineering. It determines the minimum rate at which a continuous-time signal must be sampled to be perfectly reconstructed without losing information.

The Fundamental Formula

According to the Nyquist-Shannon Theorem, to prevent aliasing, the sampling frequency ($f_s$) must be at least twice the highest frequency component ($f_{max}$) present in the signal:

$f_s \geq 2 \cdot f_{max}$

Key Definitions

• Maximum Signal Frequency ($f_{max}$): The highest frequency component of the analog signal you intend to capture.
• Nyquist Rate: The absolute minimum sampling rate ($2 \cdot f_{max}$) required to avoid aliasing.
• Nyquist Frequency: Often confused with the Nyquist rate, this is half the sampling rate ($f_s / 2$). It represents the highest frequency a given sampling system can accurately represent.
• Nyquist Interval: The maximum time interval between successive samples ($1 / f_s$).

Why is this important?

If you sample a signal at a rate lower than the Nyquist rate, aliasing occurs. Aliasing is a phenomenon where high-frequency components "fold back" into the lower frequency spectrum, creating distortion and artifacts that cannot be removed by filtering later. This is why professional audio is typically sampled at 44.1 kHz or 48 kHz—to safely cover the human hearing range which tops out at approximately 20 kHz.

Practical Example

If you are digitizing an FM radio signal with a maximum bandwidth component of 15 kHz:

1. Identify $f_{max}$: 15,000 Hz.
2. Calculate Nyquist Rate: $2 \times 15,000 = 30,000$ Hz (or 30 kHz).
3. Determine Interval: $1 / 30,000 \approx 33.33$ microseconds.

In practice, engineers often use a sampling rate slightly higher than the theoretical Nyquist rate to account for the "roll-off" of anti-aliasing filters.