I have two signals sampled at, say, 256 Hz. I want to make the difference between these two signals and downsample them, say until 32 Hz.

Is it rigourously the same (in term of final result) to make first the difference between the two original signals and then downsample OR downsample separately the two original signals and then make the difference and that's it ?

If they are not equivalent, what's the best and why ?



Basically, its equivalent, because both the downsampling process and the differencing process are linear. (If you still want peace of mind, try doing it manually both ways with a few made-up sample values.) But if there are other oddities in your system not mentioned--especially non-linear effects--then it's not so simple. For example, if the samples aren't synchronized between the two signals then the answer is more complex.

  • \$\begingroup\$ The samples are synchronized and the initial frequencies are the same, too \$\endgroup\$ – MysteryGuy Sep 6 '18 at 12:23

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