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Downsampling reduces dimensionality of the features while losing some information. It saves computation.

Upsampling brings back the resolution to the resolution of previous layer.

My question is which is better or when to use which one?

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You should use the one you need for your problem, when you know which components of your signal are of interest to you.

Let's say you have in your electronic editing an ADC digitizing 40M samples per second to study a heart rate of 70 beats per minute, you are very likely to work with useless information, that's why it will be better to down-sample your signal.

In another case, it can be very useful to oversample, some algorithms to compute an FFT work well with sample sets of power 2, it may be necessary to oversample your signal to apply a fast FFT.

That is why you should know the characteristics of your signal of interest before applying any of these functions.

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    $\begingroup$ Am I correct in saying that it’s also sometimes beneficial to upsample a signal for filtering as opposed to using a lower-fidelity version of that filter at the original sample rate? I ask because that structure is in the Oppenheim book iirc, but that may be an association with polyphase decomposition which is purely computational. $\endgroup$ – Keegs Dec 30 '20 at 15:48

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