Aliased Frequency

When a signal is sampled, the sampler cannot distinguish a tone at frequency f from tones shifted by integer multiples of the sampling rate f_s, because those versions produce the same sequence of sample values. The aliased frequency is the distance from the true frequency to the nearest such multiple, which is why n is chosen as the nearest integer to f / f_s and the absolute value is used. This gives the apparent in-band frequency you would measure after sampling, not the original frequency that was present before sampling.

Use this when analyzing sampled data for aliasing, especially in ADC design, audio, vibration, and RF undersampling problems. It is also useful for predicting what frequency a high-frequency tone will appear as after it is sampled below Nyquist.

• Using floor or ceil instead of the nearest integer for n
• Forgetting the absolute value and ending up with a negative frequency
• Confusing the aliased frequency with the original frequency or with the Nyquist frequency