Nyquist Frequency

TL;DR

• Sets the highest frequency that can be captured and reconstructed from sampled data without aliasing.
• Equals half the sampling rate (or half the bandwidth) — signals above this will be misrepresented.
• To handle higher frequencies, increase the sample rate/bandwidth or use techniques like oversampling and filtering.

Definition

The Nyquist frequency, also known as the Nyquist rate, is the maximum frequency at which a signal can be accurately sampled and reconstructed without aliasing (the phenomenon of overlapping and incorrect frequencies appearing in the reconstructed signal). It is equal to half of the sample rate or half of the bandwidth.

$$f_{\text{Nyquist}} = \frac{f_s}{2}$$

(Where f_s is the sample rate; similarly, when determined by bandwidth, f_{\text{Nyquist}} = \frac{\text{bandwidth}}{2}.)

Explanation

The Nyquist frequency defines a limit for accurate sampling and reconstruction: if sampling is performed at a rate f_s, frequency components above f_s/2 cannot be reconstructed correctly and will produce aliasing artifacts. Ensuring the sample rate or bandwidth is high enough prevents loss or distortion of high-frequency components. Practical mitigation strategies include increasing the sample rate or bandwidth, and using techniques such as oversampling or filtering to reduce aliasing and improve reconstruction quality.

Examples

Audio engineering

When recording or digitizing audio, the sample rate must be high enough to capture the signal’s frequency range. The Nyquist frequency is half the sample rate. For example, with a sample rate of 44.1kHz, the Nyquist frequency is 22.05kHz.

Radio communication

For radio transmission, the Nyquist frequency is determined by the bandwidth and equals half the bandwidth. For example, a radio signal transmitted within a bandwidth of 2MHz has a Nyquist frequency of 1MHz.

Use cases

• Telecommunications
• Radar
• Imaging

Notes or pitfalls

• If the sample rate is too low, high-frequency components are not captured accurately, causing distorted or incomplete reconstruction (aliasing).
• Receiver hardware and software limitations can prevent accurate reception of signals with frequencies above the Nyquist frequency.
• To increase the effective Nyquist frequency or mitigate aliasing: increase the sample rate or bandwidth, use oversampling, or apply filtering.

Related terms

• Nyquist rate
• Aliasing
• Sample rate
• Bandwidth
• Oversampling
• Filtering