Nyquist Frequency Aliasing Calculator and Formula

The Nyquist Frequency Aliasing Calculator helps you understand the concept of Nyquist folding or aliasing frequency in signal processing. It calculates the Nyquist frequency based on the sampling rate and shows how aliasing can impact your signals.

Nyquist Frequency and Aliasing Calculator

Example:

Input:

• Sample Rate (Fs) = 5 GSPS
• Input RF Signal Frequency (Fin) = 3.0 GHz (This is in the 2nd Nyquist Zone).

Output:

• Nyquist Frequency (Fnyquist) = 2.5 GHz
• Aliasing Frequency (Falias) = 2.0 GHz

Nyquist Frequency

The Nyquist Frequency is half of the sampling frequency. It represents the maximum frequency that can be correctly represented in a sampled signal without distortion.

The Nyquist Frequency (Fnyquist) is calculated using the formula: Fnyquist = Fs / 2

Where:

• Fnyquist is the Nyquist Frequency in Hz
• Fs is the Sampling Frequency in Hz

Why half the sampling rate?

According to the Nyquist - Shannon Sampling Theorem, to reconstruct a signal without loss, you must sample at at least twice the highest frequency component of the signal: Fs >= 2 * Fmax

Where:

• Fs is the Sampling Frequency in Hz
• Fmax is the maximum frequency component of the signal in Hz

This means that the Nyquist Frequency (Fnyquist) is the highest frequency that can be accurately represented in a sampled signal, and it is equal to half of the sampling frequency (Fs).

Aliasing Frequency (Aliasing Effect)

Aliasing occurs when a signal is sampled below the Nyquist rate, causing high frequency components to appear as lower frequencies in the sampled signal.

The Aliasing Frequency (Falias) can be calculated using the formula: Falias = |Fin - N * Fs|

Where:

• Falias is the Aliasing Frequency in Hz
• Fin is the Input RF Signal Frequency in Hz
• Fs is the Sampling Frequency in Hz
• N is an integer (the number of times the sampling frequency wraps around) N is chosen such that Falias falls within the range of 0 to Fnyquist (0 to Fs/2).

Nyquist Frequency and Aliasing Formula

Important Note

To avoid aliasing, always ensure that your sampling frequency is at least twice the highest frequency component of your signal (Fs >= 2 * Fmax). If you have a signal with frequency components above the Nyquist Frequency, consider using an anti-aliasing filter before sampling to remove those high frequency components.