Say I've got some data made from measurements with a too infrequent sampling rate; I know for certain there is aliasing. What I'm interested in is figuring out what frequencies are likely present despite aliasing.

Too start things out easy, lets say I know there are two frequencies present in the underlying signal, one aliased and one not aliased in the measurement. I also know the sampling rate. It seems like I should be able to infer the frequency of the aliased component based upon the peak frequency height of the non-aliased component and the heights and locations of the aliased component's undertones. How can I do this?

Generally, I'm interested in this type of analysis, but I've been struggling to find any resources. Are there are any texts or methods that you know of that are relevant?


1 Answer 1


In general that's not possible unless you have some additional information you can use.

Let's look at an example of a few sine wave pairs. Say 1Hz+3Hz, 1Hz+7Hz, 9Hz+7Hz, 9Hz+13Hz,11Hz+17Hz. Turns that if you sample any of these at a sample rate of 10Hz they will all result in the EXACT same discrete signal. There is no way to tell which one was sampled.

Some additional information can help. For example if you know that the spectrum is pink (falls with 3dB per octave) you could try to figure out which combination of sine waves it was by looking at the ratio of the amplitudes.

  • $\begingroup$ Are there then methods to determine possible solutions? $\endgroup$
    – Davey
    Commented Dec 27, 2023 at 0:53
  • $\begingroup$ Not without constraining the problem somehow. There is no general solution. $\endgroup$
    – Hilmar
    Commented Dec 28, 2023 at 1:53

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