Nyquist frequency

Nyquist frequency & rate

Aliasing-folding SVG

Nyquist frequency

The Nyquist frequency is a fundamental concept in the field of signal processing and digital signal processing. It is named after the Swedish-American engineer Harry Nyquist, who made significant contributions to the field of telecommunications.

Definition

The Nyquist frequency is defined as half of the sampling rate of a discrete signal processing system. It represents the highest frequency that can be accurately represented when a continuous signal is sampled. Mathematically, if the sampling rate is denoted as \( f_s \), the Nyquist frequency \( f_N \) is given by:

\[ f_N = \frac{f_s}{2} \]

Importance

The concept of the Nyquist frequency is crucial in the context of the Nyquist-Shannon sampling theorem, which states that a continuous signal can be completely represented in its sampled form and perfectly reconstructed if it is sampled at a rate greater than twice its highest frequency component. This minimum sampling rate is known as the Nyquist rate.

Aliasing

If a signal is sampled at a rate lower than the Nyquist rate, aliasing occurs. Aliasing is a phenomenon where higher frequency components of the signal are indistinguishably mapped to lower frequencies, leading to distortion and loss of information. To prevent aliasing, an anti-aliasing filter is often applied to the signal before sampling.

Applications

The Nyquist frequency is a key parameter in various applications, including:

• Digital audio and digital video processing
• Telecommunications
• Radar and sonar systems
• Medical imaging techniques such as MRI and CT scans

Related Concepts

• Sampling (signal processing)
• Nyquist-Shannon sampling theorem
• Aliasing
• Anti-aliasing filter
• Fourier transform
• Discrete Fourier transform

See Also

• Harry Nyquist
• Sampling rate
• Nyquist rate
• Signal processing
• Digital signal processing