The Nyquist frequency is one-half of the sampling rate. It is measured in samples per second and specified either in Hz/kHz/MHz/GHz or SPS/kSPS/MSPS/GSPS.

Enter the sampling rate in the calculator below, select the appropriate units and it will give the Nyquist frequency.

## Nyquist Frequency Formula

**F _{n} = F_{S}/2**

Where

**F**is the Nyquist Frequency_{n}**F**is the Sampling Rate_{S}

## Background

The Nyquist frequency [1] is an essential concept in Digital Signal Processing (DSP) [2]. It represents the highest frequency that can be accurately represented in a digital signal or waveform. It is named after Harry Nyquist [3], a Swedish-American engineer, who worked on communication theory.

According to the Nyquist-Shannon sampling theorem [4], in order to faithfully reproduce a continuous analog signal in digital form, the sampling rate must be at least twice the frequency of the highest component in the input signal.

**This means that the Nyquist frequency is half of the sampling rate. For example, if a digital signal is sampled at a rate of 5000 Hertz, the Nyquist frequency will be half that or 2500 Hertz. **

Any frequency above this threshold will result in a phenomenon called aliasing, where higher frequencies “fold back” and appear as lower frequencies. Therefore, it is important to choose an appropriate sampling rate to prevent information loss or distortion in the signal. Understanding the Nyquist frequency helps ensure accurate conversion of analog signals into digital format, enabling the faithful reproduction of the original signal.

In order to avoid aliasing, the highest frequency of the input signal should be less than or equal to the Nyquist Frequency.

*The Nyquist frequency is often confused with Nyquist rate (equal to twice the highest frequency of a given signal).*

**Example **

In this post we explained that the sampling rate of the Arduino is **15 kSPS.** The Nyquist frequency in this case is **7.5 kHz**. The frequency of an input signal cannot exceed this number if it is to be accurately represented or reconstructed.

If we are trying to sample a square wave with the Arduino, the 11th harmonic cannot be greater than the Nyquist Frequency (based on the square wave harmonics calculator). As a result the maximum frequency of a square wave input to the Arduino is **(7.5/11) kHz = 682 Hz**.

**Wikipedia References**

[3] Harry Nyquist

[4] Nyquist-Shannon Sampling Theorem