Nyquist-Shannon Sampling Rate & Aliasing Calculator
Calculate the minimum Nyquist sampling rate (fs ≥ 2f_max), Nyquist folding frequency (fs/2), anti-aliasing guard bands, and false aliased ghost frequencies.
Calculated Results
Frequently Asked Questions
What is the Nyquist-Shannon sampling theorem?
The fundamental theorem of digital signal processing states that an analog signal can be perfectly reconstructed without error if and only if it is sampled at a rate strictly greater than twice the highest frequency present: fs >= 2 × f_max.
Why was 44.1 kHz selected as the universal Compact Disc (CD) standard?
Human hearing maxes out at 20,000 Hz (20 kHz), requiring a Nyquist rate of at least 40 kHz. The extra 4.1 kHz (44.1 kHz) provides a 2,050 Hz 'guard band' allowing analog anti-aliasing low-pass filters to roll off steeply without phase distortion.
What is frequency aliasing?
If a signal is sampled below the Nyquist rate (fs < 2 f_max), high frequencies fold backwards across the Nyquist frequency (fs/2), appearing as distorted artificial 'ghost' frequencies in the audible range: f_alias = |fs - f_signal|.
How does an anti-aliasing filter prevent distortion?
An analog low-pass brickwall filter placed in front of an Analog-to-Digital Converter (ADC) attenuates all frequencies above the Nyquist limit (fs/2) before sampling occurs, ensuring no rogue frequencies fold back into the digital data.