# Nyquist Theorem

The Nyquist theorem is a fundamental result in the field of information theory, which states that a signal can be perfectly reconstructed from a sampled version of that signal if the sampling rate is greater than twice the bandwidth of the signal.

The theorem is named after Harry Nyquist, who proved the theorem in 1928.

#### What is the Nyquist theorem formula?

The Nyquist theorem is a fundamental result in the field of information theory, which states that a signal can be perfectly reconstructed from a sampled version of itself if the sampling rate is greater than twice the highest frequency component in the signal.

The theorem is named after Harry Nyquist, who first proved it in 1928.

The theorem is usually stated in the following way:

If a signal is sampled at a rate of at least 2F samples per second, where F is the highest frequency component in the signal, then the signal can be perfectly reconstructed from the samples.

The theorem is also sometimes stated in terms of the bandwidth of the signal, rather than the highest frequency component. In this case, the theorem states that a signal with a bandwidth of B can be perfectly reconstructed from a sampled version of itself if the sampling rate is greater than 2B samples per second.

It is important to note that the Nyquist theorem only applies to signals that are bandlimited, meaning that they contain no frequencies above the bandwidth B. If a signal contains frequencies above B, then it cannot be perfectly reconstructed from a sampled version of itself, regardless of the sampling rate.

The Nyquist theorem is the basis of the field of digital signal processing, and is used in a variety of applications, such as digital audio and video, radar, and telecommunications.

#### What is Nyquist sampling criteria?

The Nyquist sampling theorem states that a signal can be perfectly reconstructed from a series of samples if the sampling frequency is greater than twice the bandwidth of the signal. This theorem is also known as the Shannonâ€“Nyquist theorem, after Claude Shannon and Harry Nyquist, who both independently formulated it in the 1920s.

The theorem is named after Harry Nyquist, who published a paper in 1928 that described the phenomenon. Shannon published a similar paper in 1949, but he did not credit Nyquist.

##### What is the formula for Nyquist frequency?

The Nyquist frequency is half the sampling rate of a data signal. It is named after Harry Nyquist, who proved that a signal can be perfectly reconstructed from a sampled version of itself if the sampling rate is greater than twice the bandwidth of the signal.

#### Why do we use Nyquist frequency?

The Nyquist frequency is the highest frequency that can be accurately represented by a given data transmission system. This is due to the fact that all signals are composed of a series of sine waves, and the highest frequency that can be accurately represented by a given data transmission system is half the Nyquist frequency. This is because the highest frequency that can be accurately represented by a data transmission system is determined by the bandwidth of the system. The bandwidth of a data transmission system is the range of frequencies over which the system can operate. The Nyquist frequency is twice the bandwidth of the system.

#### Why is Nyquist criteria important?

The Nyquist criteria is important in data transmission because it provides a way to determine the maximum data rate that can be transmitted over a given channel without error. The Nyquist criteria is based on the fact that a signal can be completely reconstructed from its samples if the samples are taken at a rate that is at least twice the highest frequency component in the signal.