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If I sample a signal with a harmonic higher than half my sample frequency I can predict the aliased frequency easily as

$$|F_h-kF_s|$$

But what if after sampling the signal, I re-sample at a lower rate (decimate)?

Does the lower sampling frequency simply trump the original higher frequency or will there be mixing or modulation effects due to the two sampling frequencies that change or create new aliased harmonics?

If so, is there a way to predict what the aliased harmonics will be?

As a simple example assume I sample a signal containing a $7$ kHz harmonic at $3$ kHz, then decimate by taking every third sample, so effectively re-sampling at $1$ kHz.

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The alias behaves exactly the same, in every sense, as if it were an actual sinusoidal component at the alias frequency.

In your example, the 7 kHz harmonic sampled at 3 kHz is actually a 1 kHz sinusoid, and decimating it is exactly the same as decimating a 1 kHz signal. In this case, you end up with a DC value.

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  • $\begingroup$ So then in my example when I re-sample the 3 kHz sampled signal at 1 kHz the folding frequency (Nyquist) is pushed down to 500 Hz? If I do an FFT on the final signal would I expect to see two folding frequencies or just the final one (assuming there is wide band noise in the background that exposes folding)? $\endgroup$
    – docscience
    Commented Feb 26, 2015 at 18:18
  • $\begingroup$ @docscience, when you resample from 3 kHz to 1 kHz, the new folding frequency is 500 Hz. At any point in the system, there is only one folding frequency. $\endgroup$
    – MBaz
    Commented Feb 26, 2015 at 19:07

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