Aliasing Frequency Calculator

Find the false, folded-back frequency that appears when a signal is sampled below its Nyquist rate.

📡 Aliasing Frequency Calculator
Hz
100 Hz50,000 Hz
Hz
0 Hz50,000 Hz
Apparent (aliased) frequency
Nyquist frequency
Aliasing occurs?
Nyquist zone
Step-by-step working

📡 What is Aliasing?

Aliasing is a distortion that occurs when a signal is sampled at a rate below its Nyquist rate, the minimum rate needed to capture its highest frequency component. When this happens, frequencies above the Nyquist frequency (half the sampling rate) fold back and masquerade as false, lower-frequency content in the sampled data. The result looks like a real, valid signal, but it carries none of the original information, and there is no way to tell from the samples alone that aliasing occurred.

Aliasing shows up across engineering disciplines. Audio engineers hear it as harsh, inharmonic tones when a signal is recorded without adequate anti-aliasing filtering. Video and photography show it as moire patterns and the wagon-wheel effect where spinning wheels appear to rotate backward on camera. Instrumentation and radar systems can misreport a target's frequency entirely if their analog-to-digital converter samples too slowly for the signal bandwidth present.

A common misconception is that aliasing can be fixed after the fact with digital filtering. It cannot. Once a signal is sampled below its Nyquist rate, the true frequency information is permanently gone, replaced by the folded alias. The only defense is preventing it before sampling, with an analog anti-aliasing filter that removes energy above the Nyquist frequency before the analog-to-digital converter runs. Interestingly, some systems exploit aliasing deliberately: undersampling receivers sample a known high-frequency band on purpose to fold it down to a cheaper, lower frequency to process.

This calculator takes a sampling rate and an input signal frequency, and returns the Nyquist frequency, whether aliasing occurs, the apparent frequency an engineer would actually observe in the sampled data, and which Nyquist zone the input frequency falls into.

📐 Formula

ffolded = fin mod fs     falias = ffolded > fs/2 ? fs − ffolded : ffolded
fs = sampling rate (Hz)
fin = true input signal frequency (Hz)
fs/2 = Nyquist frequency, the highest frequency this sampling rate can capture without aliasing
falias = apparent frequency actually observed in the sampled data
Nyquist zone = floor(fin ÷ (fs/2)) + 1
Example: fs = 1,000 Hz, fin = 700 Hz → folded = 700, exceeds 500 Hz Nyquist, so alias = 1000 − 700 = 300 Hz.

📖 How to Use This Calculator

Steps

1
Enter the sampling rate. Type the sampling rate your system uses, in Hz.
2
Enter the input signal frequency. Type the true frequency of the signal being sampled, in Hz.
3
Read the results. Click Calculate to see the Nyquist frequency, whether aliasing occurs, the apparent aliased frequency, and the Nyquist zone with full folding steps.

💡 Example Calculations

Example 1 — Basic Undersampling

A 700 Hz signal sampled at 1,000 Hz

1
Nyquist frequency = 1,000 ÷ 2 = 500.00 Hz
2
700 Hz exceeds 500 Hz, so it aliases. Folded = 700 mod 1,000 = 700 Hz
3
700 > 500, so alias = 1,000 − 700 = 300.00 Hz (2nd Nyquist zone)
Apparent frequency = 300.00 Hz (aliasing occurs)
Try this example →

Example 2 — Undersampled Audio Test Tone

A 5,500 Hz test tone sampled at 8,000 Hz

1
Nyquist frequency = 8,000 ÷ 2 = 4.00 kHz
2
5,500 Hz exceeds 4,000 Hz, so it aliases. Folded = 5,500 mod 8,000 = 5,500 Hz
3
5,500 > 4,000, so alias = 8,000 − 5,500 = 2.50 kHz (2nd Nyquist zone)
Apparent frequency = 2.50 kHz (aliasing occurs)
Try this example →

Example 3 — Signal Within the Nyquist Limit

A 2,000 Hz signal sampled at 8,000 Hz, well inside the safe range

1
Nyquist frequency = 8,000 ÷ 2 = 4.00 kHz
2
2,000 Hz is below 4,000 Hz, so no aliasing occurs
3
Apparent frequency equals the true input frequency = 2.00 kHz (1st Nyquist zone)
Apparent frequency = 2.00 kHz (no aliasing)
Try this example →

❓ Frequently Asked Questions

What is aliasing in signal processing?+
Aliasing is a distortion that occurs when a signal is sampled at a rate below its Nyquist rate (twice its highest frequency component). Frequencies above the Nyquist frequency (fs/2) fold back and appear as false, lower-frequency signals mixed into the sampled data, and this corruption cannot be reversed after sampling.
How do you calculate the aliased frequency?+
Fold the input frequency into the range 0 to fs using fin mod fs, then if that folded value exceeds the Nyquist frequency (fs/2), subtract it from fs to get the apparent frequency. For fs = 1,000 Hz and fin = 700 Hz: 700 mod 1000 = 700, which exceeds 500 Hz, so the alias is 1000 - 700 = 300 Hz.
What is a Nyquist zone?+
A Nyquist zone is a frequency band of width fs/2. The 1st Nyquist zone runs from 0 to fs/2 and samples with no aliasing. The 2nd zone runs from fs/2 to fs and folds back into the 1st zone in reverse, the 3rd zone runs from fs to 3fs/2 and folds back the same direction as the original, and so on.
Can aliasing ever be useful?+
Yes. Undersampling receivers deliberately sample a known narrow high-frequency band at a rate below its actual frequency, using the predictable alias to downconvert the signal to a lower frequency for cheaper processing. This bandpass sampling technique is common in software-defined radio and some RF instrumentation.
How do you prevent aliasing?+
Sample at or above the Nyquist rate (at least twice the highest frequency present), and use an analog anti-aliasing filter before the ADC to remove any energy above the Nyquist frequency that the sampling rate cannot support. The filter must act before sampling; nothing done digitally afterward can remove aliasing that already occurred.
Why does the alias frequency sometimes equal the input frequency?+
If the input frequency is at or below the Nyquist frequency (fs/2), it falls entirely within the 1st Nyquist zone and samples correctly with no folding, so the apparent frequency equals the true input frequency. Aliasing only distorts frequencies that exceed the Nyquist frequency.
What is the difference between the Nyquist frequency and the Nyquist rate?+
The Nyquist rate is the minimum sampling rate needed for a given maximum signal frequency (2 x fmax). The Nyquist frequency is half of whatever sampling rate is actually used (fs / 2), representing the highest frequency that rate can capture without aliasing. This calculator computes the Nyquist frequency from your entered sampling rate.
What happens exactly at the Nyquist frequency?+
A signal exactly at the Nyquist frequency (fs/2) sits at the boundary between the 1st and 2nd Nyquist zones. It samples correctly in theory, but in practice it is the most fragile case: any tiny frequency drift or filter imperfection can push it into aliasing, so engineers avoid designing signals right at this edge.
Does higher sampling rate always eliminate aliasing risk?+
A higher sampling rate raises the Nyquist frequency, giving more headroom before frequencies alias, but it does not eliminate the underlying risk. Any real-world noise or interference above the new, higher Nyquist frequency will still alias unless the anti-aliasing filter is designed to remove it.
What units does this calculator use?+
Both the sampling rate and the input signal frequency are entered in hertz (Hz). Results are displayed in Hz or kHz depending on magnitude for readability, and the Nyquist zone is shown as an ordinal number (1st, 2nd, 3rd, and so on).

What is aliasing in signal processing?

Aliasing is a distortion that occurs when a signal is sampled at a rate below its Nyquist rate (twice its highest frequency component). Frequencies above the Nyquist frequency (fs/2) fold back and appear as false, lower-frequency signals mixed into the sampled data, and this corruption cannot be reversed after sampling.

How do you calculate the aliased frequency?

Fold the input frequency into the range 0 to fs using fin mod fs, then if that folded value exceeds the Nyquist frequency (fs/2), subtract it from fs to get the apparent frequency. For fs = 1,000 Hz and fin = 700 Hz: 700 mod 1000 = 700, which exceeds 500 Hz, so the alias is 1000 - 700 = 300 Hz.

What is a Nyquist zone?

A Nyquist zone is a frequency band of width fs/2. The 1st Nyquist zone runs from 0 to fs/2 and samples with no aliasing. The 2nd zone runs from fs/2 to fs and folds back into the 1st zone in reverse, the 3rd zone runs from fs to 3fs/2 and folds back in the same direction as the original, and so on.

Can aliasing ever be useful?

Yes. Undersampling receivers deliberately sample a known narrow high-frequency band at a rate below its actual frequency, using the predictable alias to downconvert the signal to a lower frequency for cheaper processing. This bandpass sampling technique is common in software-defined radio and some RF instrumentation.

How do you prevent aliasing?

Sample at or above the Nyquist rate (at least twice the highest frequency present), and use an analog anti-aliasing filter before the ADC to remove any energy above the Nyquist frequency that the sampling rate cannot support. The filter must act before sampling; nothing done digitally afterward can remove aliasing that already occurred.

Why does the alias frequency sometimes equal the input frequency?

If the input frequency is at or below the Nyquist frequency (fs/2), it falls entirely within the 1st Nyquist zone and samples correctly with no folding, so the apparent frequency equals the true input frequency. Aliasing only distorts frequencies that exceed the Nyquist frequency.

What is the difference between the Nyquist frequency and the Nyquist rate?

The Nyquist rate is the minimum sampling rate needed for a given maximum signal frequency (2 x fmax). The Nyquist frequency is half of whatever sampling rate is actually used (fs / 2), representing the highest frequency that rate can capture without aliasing. This calculator computes the Nyquist frequency from your entered sampling rate.

What happens exactly at the Nyquist frequency?

A signal exactly at the Nyquist frequency (fs/2) sits at the boundary between the 1st and 2nd Nyquist zones. It samples correctly in theory, but in practice it is the most fragile case: any tiny frequency drift or filter imperfection can push it into aliasing, so engineers avoid designing signals right at this edge.

Does higher sampling rate always eliminate aliasing risk?

A higher sampling rate raises the Nyquist frequency, giving more headroom before frequencies alias, but it does not eliminate the underlying risk. Any real-world noise or interference above the new, higher Nyquist frequency will still alias unless the anti-aliasing filter is designed to remove it.

What units does this calculator use?

Both the sampling rate and the input signal frequency are entered in hertz (Hz). Results are displayed in Hz or kHz depending on magnitude for readability, and the Nyquist zone is shown as an ordinal number (1st, 2nd, 3rd, and so on).