Sampling and aliasing calculator
A signal above half the sampling rate does not disappear. It folds back and appears at a lower frequency, indistinguishable from a real one.
Hz
Hz
Hz
Frequency it appears at
300.000Hz
- The signal will alias
- 1
- Nyquist frequency
- 500.00 Hz
- Filter attenuation at that frequency
- 20.48 dB
- Attenuation at Nyquist
- 3.88 dB
- Oversampling ratio
- 1.250
- Minimum sample rate to capture it properly
- 2600.0 Hz
Show the working
- Sample rate = 1000
- Signal frequency = 1300
- Anti-alias filter cutoff = 400
- Filter order = 2
- Nyquist frequency = 1000 / 2 = 500
- Frequency it appears at = abs(1300 - 1000 * round(1300/1000)) = 300
- The signal will alias = 1300 > 500 ? 1 : 0 = 1
- Filter attenuation at that frequency = 400 > 0 ? 20 * 2 * log10(1300/400) : 0 = 20.4753
- residual_db = -20.4753 = -20.4753
- Oversampling ratio = 400 > 0 ? 1000/(2*400) : 0 = 1.25
- Minimum sample rate to capture it properly = 1300 * 2 = 2600
- Attenuation at Nyquist = 400 > 0 ? 20 * 2 * log10(500/400) : 0 = 3.8764
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- aliased frequency = |f - fs x round(f / fs)|
- a filter of order n rolls off at 20n dB per decade
An anti-alias filter must sit before the sampler. No amount of digital filtering afterwards can undo aliasing.
Oversampling relaxes the filter requirement, which is why delta-sigma converters sample far faster than they output.