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