Nyquist Sampling Theorem Calculator

Calculate Nyquist sampling rate, oversampling ratio, aliasing frequency, ADC dynamic range, SNR, and data rate. Verify that your sampling rate satisfies the Nyquist criterion and avoid aliasing in your system.

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Formula

f_N = 2 f_{sig},\quad OSR = \frac{f_s}{f_N},\quad SNR = 6.02N + 1.76\text{ dB}

Reference: Nyquist, H. (1928). "Certain Topics in Telegraph Transmission Theory". AIEE Transactions. Shannon-Nyquist sampling theorem.

f_N — Nyquist rate (minimum sampling rate) (Hz)

f_sig — Signal maximum frequency / bandwidth (Hz)

f_s — Actual sampling rate (Sa/s)

OSR — Oversampling ratio

N — ADC resolution (bits)

SNR — Signal-to-quantization-noise ratio (dB)

How It Works

The Nyquist sampling rate theorem is a fundamental principle in signal processing that describes the minimum sampling frequency required to accurately reconstruct a continuous-time signal from its discrete samples. According to the Nyquist criterion, the sampling frequency (fs) must be at least twice the highest frequency component (fmax) present in the original analog signal. This prevents aliasing, a phenomenon where higher frequency components are misrepresented as lower frequencies when sampled inadequately. The theorem is critical in digital signal acquisition systems, including audio recording, telecommunications, medical imaging, and scientific instrumentation. The dynamic range calculation relates to analog-to-digital converter (ADC) performance, providing a theoretical maximum signal-to-noise ratio based on the number of quantization bits. This relationship demonstrates how increasing ADC resolution improves the system's ability to capture subtle signal variations with greater precision.

Worked Example

Consider an audio signal with a maximum frequency of 20 kHz, typical of human hearing. To accurately digitize this signal, the minimum sampling rate would be 40 kHz (fs = 2 × 20 kHz). Using an 16-bit ADC, the theoretical dynamic range can be calculated as 6.02 × 16 + 1.76 = 98.08 dB. If this audio signal is being recorded in stereo with 16-bit resolution, the data rate would be 40,000 Hz × 16 bits × 2 channels = 1,280,000 bits per second (1.28 Mbps).

Practical Tips

✓Use sampling rates 2.2-2.5 times the maximum signal frequency for better reconstruction
✓Implement high-order low-pass anti-aliasing filters before sampling
✓Choose ADC bit depth based on required signal-to-noise performance

Common Mistakes

✗Assuming sampling at the minimum Nyquist rate is sufficient for high-quality signal reproduction
✗Neglecting anti-aliasing filter design when implementing sampling systems
✗Overlooking quantization noise impacts in low-bit-depth ADC implementations

Frequently Asked Questions

What happens if I sample below the Nyquist rate?

Sampling below the Nyquist rate causes aliasing, where high-frequency components are incorrectly represented as lower frequencies, leading to signal distortion.

Why use more than 2x the maximum frequency?

Oversampling provides better signal reconstruction, reduces quantization noise, and allows for more robust digital filtering.

How do I choose the right ADC bit depth?

Select ADC bit depth based on the dynamic range requirements of your application, balancing signal resolution with system complexity and cost.

Can I recover aliased signals?

Once aliasing occurs, the original signal information is irrecoverably lost. Prevention through proper sampling is the only solution.

Do all signals require the same sampling approach?

Different signal types and applications have varying sampling requirements based on frequency content, noise tolerance, and reconstruction needs.